2019 JAMB Physics Past Questions — Part 2

Questions 52–101

52. 52.

    Which of the following readings cannot be determined with a meter rule?

    1. A.2.56cm
    2. B.2.25cm
    3. C.2.50cm
    4. D.2.05cm

    Show answer

    Answer: A. 2.56cm

    AI explanation

    Analysis

    The question asks us to identify which of the given measurements cannot be accurately determined using a standard meter rule. To answer this, we must look at the precision (or the smallest scale division) of a meter rule.

    Concept: Precision of a Meter Rule

    A standard meter rule is graduated in centimeters (cm) and millimeters (mm).

    • The smallest marking on a meter rule is 1 mm, which is equivalent to 0.1 cm.
    • When using a meter rule, you can read the value to the nearest millimeter (0.1 cm) with certainty, and you can estimate the next decimal place (the hundredths place) as a fraction of a millimeter (e.g., 0.05 cm).
    • However, a meter rule cannot reliably measure to two decimal places (the hundredths place) unless the value ends in .0 or .5 (representing 0 mm or half a millimeter). Any value requiring a precision beyond 0.5 mm is generally considered beyond the limit of a standard meter rule.

    Step-by-Step Evaluation

    Let's look at the options provided:

    • A. 2.56 cm: This requires measuring 0.06 cm (0.6 mm). A standard meter rule cannot accurately distinguish 0.6 mm; it can only reliably measure to the nearest 0.5 mm.
    • B. 2.25 cm: This is a value ending in .25. While some might argue it's an estimation, in the context of physics examinations, readings like 2.50 cm or 2.05 cm are standard, but 2.56 cm is physically impossible to read on a standard scale.
    • C. 2.50 cm: This is easily read as 2.5 cm on the scale.
    • D. 2.05 cm: This is read as 2.0 cm plus a half-millimeter estimation, which is standard practice.

    Comparing these, 2.56 cm is the most precise value listed that falls between the smallest readable increments of a meter rule.

    Conclusion

    This is because a meter rule is limited to a precision of 0.1 cm, and while we can estimate to 0.05 cm, we cannot reliably determine a value like 0.06 cm (the '6' in 2.56).

    Exam Tip

    Always remember the "Rule of Precision":

    • Meter Rule: Precision is 0.1 cm (or 0.05 cm by estimation).
    • Vernier Caliper: Precision is 0.01 cm.
    • Micrometer Screw Gauge: Precision is 0.001 cm. If a question asks for a measurement that seems "too precise" for a meter rule, look for the option that ends in a digit other than 0 or 5 in the hundredths place!

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53. 53.

    Which of the following characteristics of a wave is used in the measurement of the depth of the Sea?

    1. A.diffraction
    2. B.interference
    3. C.refraction
    4. D.reflection

    Show answer

    Answer: D. reflection

    AI explanation

    Analysis

    The question asks for the specific wave property utilized in sonar technology (echo sounding) to determine the depth of the ocean.

    Concept Explanation

    To measure the depth of the sea, scientists use a technique called Echo Sounding. This process involves sending a pulse of sound (usually ultrasound) from a ship down towards the seabed.

    The sound wave travels through the water, hits the ocean floor, and bounces back to the ship's receiver. This phenomenon where a wave hits a boundary and returns to the source is known as reflection. By measuring the time it takes for the pulse to return and knowing the speed of sound in water, the depth can be calculated using the formula:

    $Distance (Depth) = \frac{Speed \times Time}{2}$

    (We divide by 2 because the sound travels to the bottom and back up).

    Step-by-Step Solution

    1. Diffraction (A): This is the bending of waves around obstacles or through openings. It is not used for depth measurement.
    2. Interference (B): This occurs when two waves overlap to form a resultant wave of greater, lower, or the same amplitude. It is not the primary principle for depth measurement.
    3. Refraction (C): This is the change in direction of a wave passing from one medium to another due to a change in its speed. While sound waves do refract in water due to temperature changes, it is not the method used to measure depth.
    4. Reflection (D): As explained above, the "echo" produced when a sound wave hits the seabed and returns to the surface is a direct result of reflection. This is the fundamental principle of sonar.

    Conclusion

    Exam Tip

    Whenever you see questions about "Echoes," "Sonar," "RADAR," or "Stethoscopes," always associate them with Reflection. These are classic JAMB topics that test your understanding of how waves behave when they hit a hard surface!

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54. 54.

    When water is boiling, it

    1. A.gets hotter
    2. B.increase is mass
    3. C.decreases in mass
    4. D.changes to steam

    Show answer

    Answer: D. changes to steam

    AI explanation

    Analysis of the Question

    The question asks about the physical state of water during the process of boiling. You need to understand what happens to the molecules of water when heat is continuously applied at its boiling point.

    Explanation of the Concept

    Boiling is a phase transition process where a liquid turns into a gas (vapor) at a constant temperature known as the boiling point.

    1. Constant Temperature: Once water reaches its boiling point (100°C at standard atmospheric pressure), adding more heat does not increase the temperature of the water. Instead, the energy is used to break the intermolecular forces holding the water molecules together in the liquid state.
    2. Phase Change: As the molecules gain enough energy, they escape the surface of the liquid and enter the gaseous phase, which we call steam (or water vapor).
    3. Mass Considerations: While the mass of the water in the container decreases as it turns into steam, the fundamental physical event occurring is the change of state from liquid to gas.

    Step-by-Step Solution

    • Step 1: Evaluate Option A. Boiling occurs at a constant temperature (100°C for water). Therefore, the water does not get hotter while it is boiling.
    • Step 2: Evaluate Option B. Boiling involves the escape of molecules into the air; it does not add mass to the water.
    • Step 3: Evaluate Option C. While the mass of the liquid water decreases, this is a consequence of the process, not the definition of the process itself. The primary physical phenomenon is the change of state.
    • Step 4: Evaluate Option D. This accurately describes the phase transition that defines boiling: the conversion of liquid water into gaseous steam.

    Conclusion

    When water boils, it undergoes a phase change from liquid to gas. Therefore, the most accurate description of the process is that it changes to steam.

    Exam Tip

    Remember the "Latent Heat" rule: During any phase change (melting, boiling, freezing, or condensing), the temperature of the substance remains constant. If you see a question asking about temperature change during boiling, always remember it stays the same!

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55. 55.

    In the molecular explanation of conduction, heat is transferred by the

    1. A.Free electrons
    2. B.Free atoms
    3. C.Free molecules
    4. D.Free solids

    Show answer

    Answer: A. Free electrons

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56. 56.

    The point at which the molecules of a loaded wire begin to slide across each other resulting in a rapid increase in extension is

    1. A.yield point
    2. B.proportionality point
    3. C.deformation point
    4. D.elastic point

    Show answer

    Answer: A. yield point

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57. 57.

    A copper rod, 5m long, when heated through 10ºC, expands by 1mm. If a second copper rod, 2.5m long, is heated through 5ºC, by how much will it expand?

    1. A.4mm
    2. B.0.25mm
    3. C.2mm
    4. D.0.12mm

    Show answer

    Answer: B. 0.25mm

    AI explanation

    1. Analyze the Question

    We are given the initial length ($L_1$), the temperature change ($\Delta\theta_1$), and the expansion ($\Delta L_1$) for a copper rod. We need to find the expansion ($\Delta L_2$) for a second copper rod with a different length ($L_2$) and a different temperature change ($\Delta\theta_2$).

    2. Explain the Concept

    The linear expansion of a material is governed by the formula:

    $\Delta L = \alpha \cdot L \cdot \Delta\theta$

    Where:

    • $\Delta L$ = Change in length (expansion)
    • $\alpha$ = Coefficient of linear expansion (constant for the same material)
    • $L$ = Original length
    • $\Delta\theta$ = Change in temperature

    Since both rods are made of copper, the coefficient of linear expansion ($\alpha$) is the same for both. We can set up a ratio:

    $\frac{\Delta L_1}{L_1 \cdot \Delta\theta_1} = \frac{\Delta L_2}{L_2 \cdot \Delta\theta_2}$

    3. Show the Solution

    Given for Rod 1:

    • $L_1 = 5\text{ m}$
    • $\Delta\theta_1 = 10^\circ\text{C}$
    • $\Delta L_1 = 1\text{ mm}$

    Given for Rod 2:

    • $L_2 = 2.5\text{ m}$
    • $\Delta\theta_2 = 5^\circ\text{C}$
    • $\Delta L_2 = ?$

    Step-by-step calculation: Using the ratio formula:

    $\Delta L_2 = \Delta L_1 \times \left( \frac{L_2}{L_1} \right) \times \left( \frac{\Delta\theta_2}{\Delta\theta_1} \right)$

    Substitute the values:

    $\Delta L_2 = 1\text{ mm} \times \left( \frac{2.5}{5} \right) \times \left( \frac{5}{10} \right)$

    Simplify the fractions:

    $\Delta L_2 = 1\text{ mm} \times (0.5) \times (0.5)$

    $\Delta L_2 = 1\text{ mm} \times 0.25$

    $\Delta L_2 = 0.25\text{ mm}$

    4. Identify the Answer

    The expansion of the second rod is 0.25mm. This matches option B.

    5. Exam Tip

    When dealing with expansion problems, always check if the material is the same. If it is, $\alpha$ cancels out, and you can simply use the proportionality relationship $\Delta L \propto L \cdot \Delta\theta$. This saves you from having to calculate the actual value of $\alpha$, which is often a very small, messy decimal!

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58. 58.

    A mixture of blue and red pigment when illuminated by white light will appear

    1. A.green
    2. B.orange
    3. C.yellow
    4. D.magenta

    Show answer

    Answer: D. magenta

    AI explanation

    Analysis of the Question

    This question tests your understanding of color addition and subtraction in the context of pigments (subtractive color mixing) versus light (additive color mixing). We are looking at what happens when pigments are mixed and then illuminated by white light.

    Concept Explanation

    1. Pigments (Subtractive Mixing): Pigments work by absorbing specific wavelengths of light and reflecting others. When you mix pigments, you are essentially combining their absorption properties.
    2. Red Pigment: Absorbs all colors except red (it reflects red).
    3. Blue Pigment: Absorbs all colors except blue (it reflects blue).
    4. The Mixture: When you mix red and blue pigments, the resulting mixture absorbs almost all colors of the visible spectrum except for the red and blue light that the individual pigments reflect.
    5. Perception: When white light (which contains all colors) hits this mixture, the red pigment absorbs the non-red colors, and the blue pigment absorbs the non-blue colors. The light that is reflected to your eyes is a combination of red and blue light. In the context of color theory, the combination of red and blue light is perceived as magenta.

    Step-by-Step Solution

    • Step 1: Identify the nature of the pigments. Red pigment reflects red light; blue pigment reflects blue light.
    • Step 2: Determine the effect of mixing. Mixing pigments is a subtractive process. The mixture will reflect the colors that neither pigment absorbs.
    • Step 3: Combine the reflected colors. The mixture reflects both red and blue light.
    • Step 4: Identify the resulting color. According to the principles of color mixing, the combination of red and blue light is magenta.

    Conclusion

    When white light hits a mixture of red and blue pigments, the red and blue light are reflected back to the observer, while other colors are absorbed. This combination is perceived as magenta.

    Exam Tip

    Remember the difference between Light (Additive) and Pigments (Subtractive):

    • Light: Red + Green + Blue = White.
    • Pigments: Mixing primary pigments (Cyan, Magenta, Yellow) creates black.
    • For simple pigment mixing questions, think of the primary colors of light: Red + Blue = Magenta.

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59. 59.

    Lamps in domestic lightings are usually in

    1. A.series
    2. B.divergent
    3. C.convergent
    4. D.parallel

    Show answer

    Answer: D. parallel

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60. 60.

    When the temperature of a liquid is increased, its surface tension?

    1. A.increases
    2. B.decreases
    3. C.remain constant
    4. D.increases then decreases

    Show answer

    Answer: B. decreases

    AI explanation

    Analysis

    This question tests your understanding of the molecular behavior of liquids and the concept of surface tension in relation to thermal energy.

    Concept Explanation

    Surface tension is the result of cohesive forces between molecules at the surface of a liquid. These molecules are pulled inward by the molecules beneath them, creating a "skin" or tension.

    When you increase the temperature of a liquid:

    1. Increased Kinetic Energy: The molecules gain more kinetic energy and move faster.
    2. Weakened Cohesive Forces: As the molecules move more vigorously, the intermolecular forces (cohesive forces) that hold them together become weaker.
    3. Reduced Tension: Since surface tension is directly dependent on the strength of these cohesive forces, as the forces weaken, the surface tension of the liquid decreases.

    Step-by-Step Solution

    1. Identify the relationship: Surface tension is a measure of the strength of the attractive forces between liquid molecules.
    2. Apply heat: Adding heat increases the thermal agitation of the molecules.
    3. Observe the effect: This agitation disrupts the orderly arrangement and the strength of the intermolecular bonds at the surface.
    4. Conclusion: Because the bonds are weakened by the increased temperature, the surface tension must decrease.

    Exam Tip

    Think of surface tension like a "tightly knit group of friends holding hands." If you make them run around and get very excited (increase temperature), they won't be able to hold onto each other as tightly. Therefore, the "tension" in their grip decreases!

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61. 61.

    Three resistors with resistance 200Ω, 500Ω and 1kΩ are connected in series. A 6v battery is connected to either end of the combination. Calculate the potential difference between the ends of 200Ω resistance.

    1. A.0.71V
    2. B.0.7V
    3. C.0.82V
    4. D.0.8V

    Show answer

    Answer: A. 0.71V

    AI explanation

    1. Analyze the Question

    We are given three resistors connected in series: $R_1 = 200\,\Omega$, $R_2 = 500\,\Omega$, and $R_3 = 1000\,\Omega$ (since $1\text{k}\Omega = 1000\,\Omega$). They are connected to a $6\text{V}$ battery. We need to find the potential difference (voltage drop) across the $200\,\Omega$ resistor.

    2. Explain the Concept

    • Series Circuit: In a series circuit, the current ($I$) flowing through each resistor is the same.
    • Total Resistance ($R_T$): For resistors in series, $R_T = R_1 + R_2 + R_3$.
    • Ohm's Law: $V = IR$, where $V$ is voltage, $I$ is current, and $R$ is resistance.
    • Voltage Divider Rule: The voltage across a specific resistor in a series circuit is proportional to its resistance relative to the total resistance: $V_x = V_{total} \times \frac{R_x}{R_T}$.

    3. Show the Solution

    Step 1: Calculate the total resistance ($R_T$)

    $R_T = 200\,\Omega + 500\,\Omega + 1000\,\Omega = 1700\,\Omega$

    Step 2: Calculate the total current ($I$) in the circuit Using Ohm's Law ($I = \frac{V}{R_T}$):

    $I = \frac{6\text{V}}{1700\,\Omega} \approx 0.003529\text{A}$

    Step 3: Calculate the potential difference across the $200\,\Omega$ resistor ($V_{200}$) Using Ohm's Law ($V = IR$):

    $V_{200} = I \times R_1$

    $V_{200} = 0.003529\text{A} \times 200\,\Omega$

    $V_{200} \approx 0.7058\text{V}$

    Rounding to two decimal places, we get 0.71V.

    4. Identify the Answer

    Comparing our result to the given options, the value matches option A.

    5. Exam Tip

    When dealing with series circuits, always remember that the largest resistor will always have the largest voltage drop across it. If you ever get a voltage drop that is higher than the battery's total voltage, you know you've made a calculation error!

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62. 62.

    A mass of 0.5kg is whirled in a vertical circle of radius 2m at a steady rate of 2 rev/s. Calculate the centripetal force

    1. A.164N
    2. B.160N
    3. C.158N
    4. D.172N

    Show answer

    Answer: C. 158N

    AI explanation

    1. Analyze the question

    We are given:

    • Mass ($m$) = 0.5 kg
    • Radius ($r$) = 2 m
    • Frequency ($f$) = 2 rev/s
    • We need to find the Centripetal Force ($F_c$).

    2. Explain the concept

    Centripetal force is the force required to keep an object moving in a circular path. The formula is:

    $F_c = m \omega^2 r$

    Where:

    • $m$ is the mass
    • $r$ is the radius
    • $\omega$ (omega) is the angular velocity, where $\omega = 2\pi f$

    Substituting $\omega$ into the force formula, we get:

    $F_c = m(2\pi f)^2 r = 4\pi^2 f^2 mr$

    3. Show the solution

    • Step 1: Identify the values: $m = 0.5$, $r = 2$, $f = 2$.
    • Step 2: Use the formula $F_c = 4\pi^2 f^2 mr$.
    • Step 3: Substitute the values: $$F_c = 4 \times (\pi^2) \times (2^2) \times 0.5 \times 2$$ $$F_c = 4 \times \pi^2 \times 4 \times 1$$ $$F_c = 16 \times \pi^2$$
    • Step 4: Using $\pi \approx 3.142$, then $\pi^2 \approx 9.87$: $$F_c = 16 \times 9.87 = 157.92 \text{ N}$$

    Rounding to the nearest whole number, we get 158 N.

    4. Identify the answer

    Comparing our result to the options provided, 158 N matches option C.

    5. Tip

    In JAMB Physics, when you see "rev/s" (revolutions per second), always remember that this is your frequency ($f$). If the question had said "rad/s," that would be your angular velocity ($\omega$) directly. Also, always keep $\pi^2 \approx 9.87$ or $10$ in mind, as it often helps simplify calculations in multiple-choice questions.

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63. 63.

    When a girl moves towards a plane mirror at a speed of 4.0m/s, the distance between the girl & her image reduces at a speed of

    1. A.2 m/s
    2. B.4 m/s
    3. C.8 m/s
    4. D.12 m/s

    Show answer

    Answer: C. 8 m/s

    AI explanation

    Analysis

    This question tests your understanding of the properties of plane mirrors, specifically the relationship between the motion of an object and the motion of its image.

    Concept

    In a plane mirror, the image is always formed at the same distance behind the mirror as the object is in front of it.

    • If the object moves towards the mirror at a speed $v$, the image also moves towards the mirror at the same speed $v$.
    • However, the question asks for the speed at which the distance between the girl and her image reduces. Since both the girl and the image are moving towards each other, their relative speed is the sum of their individual speeds.

    Step-by-Step Solution

    1. Identify the speed of the girl ($v_g$): The girl moves towards the mirror at $4.0\text{ m/s}$.
    2. Identify the speed of the image ($v_i$): Because the image moves at the same speed as the object relative to the mirror, the image also moves towards the mirror at $4.0\text{ m/s}$.
    3. Calculate the relative speed: Since the girl and the image are moving towards each other, the rate at which the gap between them closes is the sum of their speeds: $$\text{Relative speed} = v_g + v_i$$ $$\text{Relative speed} = 4.0\text{ m/s} + 4.0\text{ m/s}$$ $$\text{Relative speed} = 8.0\text{ m/s}$$

    Conclusion

    The distance between the girl and her image reduces at a speed of $8.0\text{ m/s}$.

    Exam Tip

    Always remember the "Double Rule" for plane mirrors:

    • If an object moves towards a mirror at speed $v$, the image moves towards the object at $2v$.
    • If you rotate a plane mirror by an angle $\theta$, the reflected ray rotates by $2\theta$. Keeping these "doubling" effects in mind will help you solve similar mirror problems quickly in the exam hall!

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64. 64.

    A force of 6N acts horizontally on a stationary mass of 2kg for 4s. The kinetic energy gained by the mass is _________

    1. A.366j
    2. B.240j
    3. C.144j
    4. D.90j

    Show answer

    Answer: C. 144j

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65. 65.

    Which of the following statement about the electromagnet shown above is correct?

    1. A.when the current flows from A to B, the end A will be in north pole
    2. B.when the current flows from A to B, the end A will be south pole
    3. C.when the current flows from A to B, the end B will be south pole
    4. D.none of the above

    Show answer

    Answer: C. when the current flows from A to B, the end B will be south pole

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66. 66.

    The diagram shows four positions of the bob of a simple pendulum. At which of these positions does the bob have maximum kinetic energy and minimum potential energy

    1. A.1
    2. B.2
    3. C.None Of The Above
    4. D.4

    Show answer

    Answer: B. 2

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67. 67.

    A supply of 400V is connected across capacitors of 3μf and 6μf in series. Calculate the charge

    1. A.8 x 10$^{-4}$C
    2. B.4 x 10$^{-2}$C
    3. C.8 x 10$^{-3}$C
    4. D.4 x 10$^{-8}$C

    Show answer

    Answer: A. 8 x 10$^{-4}$C

    AI explanation

    Analysis

    To solve this problem, we need to understand how capacitors behave when connected in series and how to calculate the total charge stored in the circuit.

    Concept

    1. Capacitors in Series: When capacitors are connected in series, the total (equivalent) capacitance ($C_T$) is calculated using the formula: $$\frac{1}{C_T} = \frac{1}{C_1} + \frac{1}{C_2}$$Alternatively, for two capacitors:$C_T = \frac{C_1 \times C_2}{C_1 + C_2}$
    2. Charge Formula: The total charge ($Q$) in a capacitor circuit is given by: $$Q = C_T \times V$$Where$V$ is the supply voltage. In a series circuit, the charge on each capacitor is the same as the total charge supplied by the source.

    Step-by-Step Solution

    Step 1: Calculate the equivalent capacitance ($C_T$) Given: $C_1 = 3\mu F$ and $C_2 = 6\mu F$

    $C_T = \frac{3 \times 6}{3 + 6} = \frac{18}{9} = 2\mu F$

    Convert microfarads to farads: $2\mu F = 2 \times 10^{-6} F$

    Step 2: Calculate the total charge ($Q$) Given: $V = 400V$

    $Q = C_T \times V$

    $Q = (2 \times 10^{-6} F) \times 400V$

    $Q = 800 \times 10^{-6} C$

    Step 3: Express in standard form

    $Q = 8 \times 10^2 \times 10^{-6} C$

    $Q = 8 \times 10^{-4} C$

    Conclusion

    Comparing our result to the options provided, the calculated charge is $8 \times 10^{-4} C$. This matches option A.

    Exam Tip

    When capacitors are in series, the equivalent capacitance is always smaller than the smallest individual capacitor in the circuit. If you ever calculate a total capacitance larger than your smallest capacitor, double-check your math! Also, remember that in series, the charge ($Q$) is constant across all capacitors, but the voltage ($V$) is divided.

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68. 68.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

69. 69.

    Which of the following media allow the transmission of sound waves through them? I. air II. liquid III. solids

    1. A.I & II only
    2. B.I & III only
    3. C.II & III only
    4. D.I, II & III

    Show answer

    Answer: D. I, II & III

    AI explanation

    1. Analyze the question

    The question asks us to identify which of the listed media (air, liquid, and solids) can transmit sound waves.

    2. Explain the concept

    Sound is a mechanical wave. Unlike light, which can travel through a vacuum, mechanical waves require a material medium to propagate.

    Sound travels by the vibration of particles. When a sound source vibrates, it causes the particles of the medium around it to vibrate. These particles then collide with their neighbors, transferring the energy of the wave forward.

    • Solids: Particles are very close together, making it the fastest medium for sound transmission.
    • Liquids: Particles are closer than in gases, allowing sound to travel faster than in air.
    • Gases (like air): Particles are further apart, making it the slowest medium for sound transmission, but it still allows for the movement of sound waves.

    Since sound requires a medium to travel, it can pass through any state of matter (solid, liquid, or gas) as long as particles are present to carry the vibration.

    3. Show the solution

    • I. Air (Gas): Sound travels through air (e.g., hearing someone speak).
    • II. Liquid: Sound travels through liquids (e.g., whales communicating underwater).
    • III. Solids: Sound travels through solids (e.g., placing your ear against a wall to hear a sound on the other side).

    Since sound waves can travel through all three states of matter, all the listed options are correct.

    4. Identify the answer

    The correct option is D, which includes I, II, and III.

    5. Exam Tip

    Remember the acronym "S-L-G" (Solid, Liquid, Gas). Sound travels fastest in solids and slowest in gases. A common JAMB trick is to ask where sound cannot travel; the answer is always a vacuum (like outer space) because there are no particles to vibrate!

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70. 70.

    Which of the following is/are the limitations to the Rutherford's atomic models? I. It is applicable when energy is radiated as electrons are revolving II. It is applicable when energy is radiated in a continuous mode III. It is applicable to an atom with only one electron in the other shell

    1. A.I only
    2. B.II only
    3. C.I & II only
    4. D.I, II & III only

    Show answer

    Answer: C. I & II only

    AI explanation

    Analysis of the Question

    This question tests your understanding of the historical development of atomic theory, specifically the flaws in Ernest Rutherford’s model of the atom (the "planetary model").

    Concept Explanation

    Rutherford proposed that electrons orbit the nucleus like planets orbit the sun. However, classical physics (Maxwell’s electromagnetic theory) presented two major problems for this model:

    1. The Stability Problem: According to classical physics, an accelerating charged particle (like an electron moving in a circular orbit) must continuously radiate energy. If the electron radiates energy, it should lose speed, spiral inwards, and eventually crash into the nucleus. Rutherford’s model could not explain why atoms are stable.
    2. The Continuous Spectrum Problem: If the electron were to radiate energy continuously, the spectrum emitted by the atom should be a continuous spectrum (all colors blending into each other). However, experiments showed that atoms emit line spectra (discrete, specific wavelengths).

    Because Rutherford’s model assumed continuous radiation, it failed to account for the stability of the atom and the discrete nature of atomic spectra. Bohr later corrected this by proposing that electrons exist in "stationary orbits" where they do not radiate energy.

    Step-by-Step Solution

    • Statement I: "It is applicable when energy is radiated as electrons are revolving." This is a limitation. Rutherford’s model assumed electrons radiate energy while revolving, which leads to the collapse of the atom. Since atoms don't collapse, this assumption is incorrect.
    • Statement II: "It is applicable when energy is radiated in a continuous mode." This is a limitation. Rutherford’s model implies a continuous emission of energy, but experimental evidence shows that atoms emit discrete (line) spectra, not continuous ones.
    • Statement III: "It is applicable to an atom with only one electron in the other shell." This is actually a success (or a specific condition) of the Bohr model, not a limitation of Rutherford's. Rutherford's model was fundamentally flawed for all atoms because it couldn't explain stability.

    Since Statements I and II describe the theoretical failures (limitations) of the Rutherford model, they are the correct limitations.

    Conclusion

    The limitations are found in statements I and II. Therefore, the correct option is C.

    Exam Tip

    When you see questions about atomic models, remember the "Bohr Correction":

    • Rutherford: Electrons orbit like planets (failed because it predicted the atom would collapse).
    • Bohr: Electrons orbit in fixed energy levels (stationary states) where they do not radiate energy. They only radiate energy when they jump between levels.

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71. 71.

    Aluminium is sometimes used as the leaf of an electroscope because it

    1. A.is a light material
    2. B.is a good conductor
    3. C.is a good insulator
    4. D.can be converted into thin sheets

    Show answer

    Answer: A. is a light material

    AI explanation

    Analysis

    The question asks for the specific physical property of aluminium that makes it suitable for use as the leaf of a gold-leaf electroscope.

    Concept Explanation

    An electroscope is a device used to detect the presence of electric charge. It consists of a metal rod with a thin, flexible metal leaf (traditionally gold, but often aluminium in modern school laboratories) attached to the bottom.

    For an electroscope to function effectively:

    1. Charge Distribution: The material must be a conductor so that the electric charge can flow from the cap down to the leaf.
    2. Sensitivity: The leaf must be extremely light so that even a very small amount of charge (which creates a small electrostatic force) can cause the leaf to deflect or move away from the metal rod.

    Step-by-Step Solution

    1. Evaluate Option C: Aluminium is a metal, not an insulator. An insulator would not allow charge to flow to the leaf, so the electroscope would not work. This is incorrect.
    2. Evaluate Option D: While it is true that aluminium is malleable (can be made into thin sheets), this is a property of many metals. It explains how we make the leaf, but not why it is the best choice for the function of the device.
    3. Evaluate Option B: Aluminium is a good conductor, which is necessary. However, if it were heavy, it would require a large force to move, making the electroscope insensitive to small charges.
    4. Evaluate Option A: The primary reason for choosing aluminium (or gold) is its low density and ability to be beaten into an extremely thin, light foil. Because the leaf is so light, the electrostatic repulsion between the rod and the leaf is sufficient to cause a visible deflection even with a tiny charge. In the context of physics examinations, "lightness" is the critical factor that ensures high sensitivity.

    Conclusion

    While aluminium is a conductor, its primary advantage as an electroscope leaf—compared to other conductors—is its extremely low mass (lightness), which allows it to respond to the smallest electrostatic forces.

    Exam Tip

    When you see questions about electroscope leaves, remember the "Sensitivity Rule": The leaf must be light to detect small charges and a conductor to allow charge flow. If both "light" and "conductor" are options, "light" is usually the intended answer because it explains the sensitivity of the instrument.

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72. 72.

    The mass of a nucleus is the

    1. A.total number of its proton & neutrons
    2. B.number of its protons
    3. C.mass of its electrons
    4. D.total number of its protons & electrons

    Show answer

    Answer: A. total number of its proton & neutrons

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73. 73.

    During the transformation of matter from the solid to the liquid state, the heat supplied does not produce a temperature increase because

    1. A.the heat energy is quickly conducted away
    2. B.the heat capacity has become very large as the substance melts
    3. C.the heat gained is equal to the heat lost by the substance
    4. D.all the heat is used to break the bonds holding the molecules of the solid together

    Show answer

    Answer: D. all the heat is used to break the bonds holding the molecules of the solid together

    AI explanation

    1. Analyze the Question

    The question asks why the temperature of a substance remains constant during the phase change from solid to liquid (melting), even though heat is being continuously supplied to it.

    2. Explain the Concept

    In physics, this phenomenon is known as Latent Heat of Fusion.

    When a substance is in a solid state, its molecules are held together in a fixed, rigid structure by strong intermolecular forces. To transition from a solid to a liquid, these bonds must be overcome.

    When you supply heat to a melting solid:

    • The energy is not used to increase the kinetic energy of the molecules (which is what would cause a rise in temperature).
    • Instead, the energy is used entirely to perform the work of breaking or weakening the intermolecular bonds that hold the solid structure together.
    • Because the kinetic energy of the molecules remains unchanged during this process, the temperature remains constant until the entire substance has melted.

    3. Show the Solution

    • Step 1: Recognize that temperature is a measure of the average kinetic energy of the particles in a substance.
    • Step 2: Identify that during a phase change (like melting), the substance is absorbing energy (latent heat).
    • Step 3: Apply the principle of conservation of energy: Since the temperature is not rising, the energy supplied must be going into potential energy (breaking bonds) rather than kinetic energy.
    • Step 4: Evaluate the options. Options A, B, and C describe processes that do not explain the constant temperature during phase change. Option D correctly identifies that the energy is consumed by the structural changes (breaking bonds).

    4. Identify the Answer

    The correct option is D. All the heat energy supplied is used as latent heat to overcome the intermolecular forces, allowing the solid to transition into a liquid without increasing the temperature.

    5. Exam Tip

    Remember the phrase: "Latent means hidden." When you see a flat line on a temperature-time graph during a phase change, know that the heat is "hidden" because it is working on the bonds, not the thermometer!

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74. 74.

    The limiting frictional force between two surface depends on I. the gaseous reaction between the surfaces II. the nature of the surfaces in contact III. the relative velocity between the surfaces

    1. A.I only
    2. B.I & IV only
    3. C.II only
    4. D.III only

    Show answer

    Answer: C. II only

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75. 75.

    The volume of a stone having an irregular shape can be determined using?

    1. A.meter rule
    2. B.measuring cylinder
    3. C.vernier calliper
    4. D.micrometer screw gauge

    Show answer

    Answer: B. measuring cylinder

    AI explanation

    Analysis

    The question asks for the appropriate instrument used to measure the volume of an object with an irregular shape. Unlike regular shapes (like cubes or spheres) where you can measure dimensions and use a formula, irregular objects do not have specific dimensions to measure with a ruler or gauge.

    Concept: Displacement Method

    To find the volume of an irregular solid, we use the Archimedes' Principle or the displacement method.

    1. You fill a container (like a measuring cylinder) with a known volume of liquid (usually water).
    2. You submerge the irregular object completely into the liquid.
    3. The object displaces a volume of water equal to its own volume.
    4. The new reading on the scale minus the initial reading gives you the volume of the stone.

    Step-by-Step Solution

    1. Analyze the options: • A. Meter rule: Used for measuring length, width, or height of regular objects. • B. Measuring cylinder: A graduated glass or plastic container used to measure the volume of liquids and, by displacement, the volume of irregular solids. • C. Vernier calliper: Used for measuring small lengths, internal/external diameters, and depths of objects with high precision. • D. Micrometer screw gauge: Used for measuring very small lengths or thicknesses with extremely high precision.

    2. Evaluate: Since the stone is irregular, you cannot measure its "length" or "diameter" to calculate volume. You must use the displacement of a liquid. The measuring cylinder is specifically designed for this purpose.

    Conclusion

    The measuring cylinder is the correct tool because it allows you to observe the rise in water level caused by the submerged stone, which directly corresponds to the stone's volume.

    Exam Tip

    Whenever you see a question about measuring the volume of an irregular object, always look for keywords like "displacement," "measuring cylinder," or "eureka can." These are the standard tools for this task in Physics practicals.

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76. 76.

    The limiting frictional force between two surfaces depends on I. the cohesive force of the material II. the nature of the surfaces in contact III. the relative velocity between the surfaces

    1. A.I only
    2. B.II only
    3. C.III only
    4. D.I & IV only

    Show answer

    Answer: B. II only

    AI explanation

    Analysis of the Question

    The question asks us to identify the factors that influence the limiting frictional force (the maximum static friction) between two surfaces. We need to evaluate the three statements provided:

    • I. The cohesive force of the material: This relates to the molecular attraction between the surfaces.
    • II. The nature of the surfaces in contact: This refers to the roughness or smoothness of the surfaces (often represented by the coefficient of friction, $\mu$).
    • III. The relative velocity between the surfaces: This refers to how fast one surface is moving over the other.

    Concept Explanation

    Friction is a force that opposes motion. The limiting frictional force ($F_L$) is defined by the formula:

    $F_L = \mu R$

    Where:

    • $\mu$ (Coefficient of friction): This is determined by the nature of the surfaces in contact (e.g., wood on wood vs. steel on ice).
    • $R$ (Normal reaction): This is the force pressing the two surfaces together.

    Evaluating the statements:

    1. Cohesive force (I): While molecular forces contribute to the nature of the surface, "limiting friction" in standard physics curricula is primarily defined by the nature of the surfaces and the normal reaction, not the cohesive force of the bulk material itself.
    2. Nature of the surfaces (II): This is the primary factor. Different materials have different coefficients of friction ($\mu$). This is definitely a factor.
    3. Relative velocity (III): Limiting friction is the force required to start motion. Once motion begins, we talk about kinetic friction. The limiting frictional force is independent of the speed or relative velocity between the surfaces.

    Step-by-Step Solution

    • Step 1: Identify the formula for limiting friction: $F_L = \mu R$.
    • Step 2: Analyze the variables. $\mu$ depends on the nature of the surfaces (Statement II). $R$ depends on the weight or applied pressure.
    • Step 3: Compare with the options. Statement II is correct. Statement III is incorrect because limiting friction is independent of velocity (it is a static condition). Statement I is generally considered a property of the material's surface, but in the context of standard JAMB physics, the "nature of the surfaces" is the standard accepted factor.
    • Step 4: Looking at the options provided, Option B (II only) is the most accurate representation of the factors affecting limiting friction.

    Conclusion

    The limiting frictional force is independent of the area of contact and the relative velocity. It depends on the nature of the surfaces (the coefficient of friction) and the normal reaction. Therefore, only statement II is correct.

    Exam Tip: Always remember that friction is independent of the surface area and independent of the velocity of the sliding object. If you see these in a question, you can immediately rule them out!

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77. 77.

    The mass of water vapour in a given volume of air is 0.05g at 20°C, while the mass of water vapour required to saturate it at the same temperature is 0.15g. Calculate the relative humidity of the air.

    1. A.3.33%
    2. B.5.55%
    3. C.33.33%
    4. D.55.55%

    Show answer

    Answer: C. 33.33%

    AI explanation

    1. Analyze the question

    We are asked to calculate the relative humidity of a sample of air. We are given:

    • Mass of water vapour present (actual mass): $0.05\text{ g}$
    • Mass of water vapour required to saturate the air (saturated mass): $0.15\text{ g}$

    2. Explain the concept

    Relative Humidity (RH) is defined as the ratio of the actual mass of water vapour present in a given volume of air to the mass of water vapour required to saturate the same volume of air at the same temperature. It is usually expressed as a percentage.

    The formula is:

    $\text{Relative Humidity} = \frac{\text{Mass of water vapour present}}{\text{Mass of water vapour required to saturate}} \times 100\%$

    3. Show the solution

    • Step 1: Identify the given values. • Actual mass = $0.05\text{ g}$ • Saturated mass = $0.15\text{ g}$

    • Step 2: Substitute the values into the formula. $$\text{RH} = \left( \frac{0.05}{0.15} \right) \times 100\%$$

    • Step 3: Simplify the fraction. $$\frac{0.05}{0.15} = \frac{5}{15} = \frac{1}{3}$$

    • Step 4: Calculate the final percentage. $$\text{RH} = \frac{1}{3} \times 100\%$$ $$\text{RH} = 33.333...\%$$

    Rounding to two decimal places, we get 33.33%.

    4. Identify the answer

    Comparing our result to the given options: A. 3.33% B. 5.55% C. 33.33% D. 55.55%

    The correct option is C.

    5. Tip

    When calculating relative humidity, always remember that the "saturated" value must be the larger number (the denominator). If you ever get a percentage greater than 100%, you have likely swapped the numerator and the denominator! Also, remember that relative humidity is a ratio, so the units (grams) cancel out, leaving you with a dimensionless percentage.

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78. 78.

    Efficiency of conduction in liquids and gases compared to solids is

    1. A.less efficient than solid
    2. B.more efficient than solids
    3. C.equally efficient to solids
    4. D.efficiently may vary

    Show answer

    Answer: A. less efficient than solid

    AI explanation

    Analysis of the Question

    The question asks for a comparison of the efficiency of heat conduction between liquids/gases and solids. To answer this, we must understand the mechanism of heat transfer through conduction at the molecular level.

    Concept Explanation

    Conduction is the process of heat transfer through a material without the actual movement of the material itself. It occurs primarily through two mechanisms:

    1. Molecular Vibration: Particles vibrate and collide with neighboring particles, passing kinetic energy along.
    2. Free Electrons: In metals (solids), free electrons move rapidly through the lattice structure, carrying thermal energy much faster than molecular vibrations alone.

    • In Solids: Particles are packed very closely together in a fixed, orderly lattice. This proximity allows for rapid transfer of energy through collisions and, in the case of metals, the movement of free electrons.
    • In Liquids and Gases: Particles are much further apart (especially in gases). Because there is more space between molecules, the frequency of collisions is significantly lower, making them very poor conductors of heat compared to solids. In fact, liquids and gases are often referred to as insulators because they conduct heat so poorly.

    Step-by-Step Solution

    1. Identify the medium: Solids have a dense, rigid structure that facilitates the rapid transfer of kinetic energy.
    2. Compare with fluids: Liquids and gases have molecules that are loosely packed and move randomly. The distance between these molecules makes the transfer of energy via collision much slower.
    3. Conclusion: Because the molecular structure of solids allows for more frequent and effective collisions (and the presence of free electrons in metals), solids are much better conductors of heat than liquids and gases.
    4. Result: Therefore, the efficiency of conduction in liquids and gases is significantly lower than in solids.

    Exam Tip

    Think of a crowded room (a solid): if you tap the person next to you, the message travels instantly. Now think of a room where people are standing far apart (a gas): you have to walk across the room to tap the next person, which takes much longer. That is why solids conduct heat faster!

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79. 79.

    A ray of light passes through the centre of curvature of a concave mirror and strikes the mirror. At what angle is the ray reflected?

    1. A.180$^o$
    2. B.90$^o$
    3. C.0$^o$
    4. D.60$^o$

    Show answer

    Answer: C. 0$^o$

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80. 80.

    The equilibrium position of objects in any field corresponds to situation of

    1. A.equipotential energy
    2. B.maximum potential energy
    3. C.minimum potential energy
    4. D.minimum kinetic energy

    Show answer

    Answer: C. minimum potential energy

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81. 81.

    A single force which produces the same effect as a set of forces acting together at a point is known as the

    1. A.component
    2. B.equilibrant
    3. C.resultant
    4. D.resistant

    Show answer

    Answer: C. resultant

    AI explanation

    Analysis

    The question asks for the definition of a specific term in mechanics that describes a single force capable of replacing a group of forces while producing the exact same physical effect (acceleration or state of motion) on a body.

    Concept Explanation

    In physics, when several forces act on an object simultaneously, they can be combined into one single force.

    • Resultant Force: This is the vector sum of all the individual forces acting on a body. It represents the "net" effect of those forces. If you replace all the individual forces with this single resultant force, the object will behave in exactly the same way.
    • Equilibrant Force: This is a force equal in magnitude to the resultant force but acting in the opposite direction. Its purpose is to bring the system into equilibrium (i.e., to make the net force zero).
    • Component: These are the individual parts into which a single force can be broken down (usually along the x and y axes).

    Step-by-Step Solution

    1. Identify the goal: We are looking for a term that represents the "combined effect" of multiple forces.
    2. Evaluate the options: • A (Component): This is the reverse of our goal; it is a part of a force, not the whole. • B (Equilibrant): This force cancels out the effect of other forces; it does not produce the same effect as them. • C (Resultant): By definition, the resultant is the single force that represents the combined vector sum of all forces acting on a point. • D (Resistant): This is not a standard term used in this context in mechanics.
    3. Conclusion: The resultant force is the single force that produces the same effect as the set of forces acting together.

    Final Answer

    The correct option is C.

    Exam Tip

    Think of the Resultant as the "Result" of adding all forces together, and the Equilibrant as the "Equalizer" that brings everything to a stop (equilibrium). Don't mix them up!

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82. 82.

    An object is acted upon by a system of parallel forces causing the object to be in state equilibrium. Which of the following statement is not correct

    1. A.the resultant of the parallel forces is zero
    2. B.the algebraic sum of all the moments of the forces is zero
    3. C.all the parallel forces must not be equal in magnitude and direction
    4. D.the sum of forces in one direction must be equal to the sum of forces in the opposite direction

    Show answer

    Answer: C. all the parallel forces must not be equal in magnitude and direction

    AI explanation

    Analysis

    To solve this problem, we need to understand the conditions required for an object to be in equilibrium under a system of parallel forces.

    Concept: Conditions for Equilibrium

    For a body to be in equilibrium, two primary conditions must be satisfied:

    1. Translational Equilibrium: The vector sum of all forces acting on the body must be zero ($\sum F = 0$). This means the sum of forces acting in one direction must be exactly balanced by the sum of forces acting in the opposite direction.
    2. Rotational Equilibrium: The algebraic sum of the moments of all forces about any point must be zero ($\sum M = 0$).

    Step-by-Step Evaluation

    • Option A: "The resultant of the parallel forces is zero." This is correct. If the resultant were not zero, the object would accelerate in the direction of the resultant force.
    • Option B: "The algebraic sum of all the moments of the forces is zero." This is correct. This is the condition for rotational equilibrium.
    • Option C: "All the parallel forces must not be equal in magnitude and direction." This statement is incorrect. In a system of parallel forces, it is perfectly possible for forces to have equal magnitudes and directions (e.g., two equal upward forces balancing a downward weight). There is no rule stating they must not be equal; they simply need to satisfy the equilibrium conditions.
    • Option D: "The sum of forces in one direction must be equal to the sum of forces in the opposite direction." This is correct. This is simply another way of stating that the resultant force is zero (as mentioned in Option A).

    Conclusion

    The question asks which statement is not correct. Since options A, B, and D are fundamental requirements for equilibrium, Option C is the statement that does not hold true as a rule.

    *

    Exam Tip

    When dealing with equilibrium questions, always remember the "Zero Rule":

    • Sum of Forces = 0
    • Sum of Moments = 0 If any option suggests a non-zero value for these, it is usually the "incorrect" statement you are looking for!

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83. 83.

    A thermocouple thermometer is connected to a millivoltmeter which can read up to 10mV. When one junction is in ice at 0°C and the other is steam at 100°C, the millivoltmeter reads 4mV. What is the maximum temperature which this arrangement can measure

    1. A.100$^o$C
    2. B.248$^o$C
    3. C.250$^o$C
    4. D.350$^o$C

    Show answer

    Answer: C. 250$^o$C

    AI explanation

    Analysis

    To solve this problem, we need to understand the relationship between the electromotive force (e.m.f.) produced by a thermocouple and the temperature difference between its junctions. For most thermocouples within a reasonable range, the e.m.f. ($E$) is directly proportional to the temperature difference ($\Delta\theta$) between the cold junction and the hot junction.

    Concept

    The formula for this linear relationship is:

    $E = k \times (\theta_h - \theta_c)$

    Where:

    • $E$ = e.m.f. in millivolts (mV)
    • $k$ = a constant for the thermocouple
    • $\theta_h$ = temperature of the hot junction
    • $\theta_c$ = temperature of the cold junction (in this case, 0°C)

    Step-by-Step Solution

    Step 1: Find the constant ($k$) using the given data. We are told that when the hot junction is at 100°C and the cold junction is at 0°C, the reading is 4mV.

    $4\text{mV} = k \times (100^\circ\text{C} - 0^\circ\text{C})$

    $4 = k \times 100$

    $k = \frac{4}{100} = 0.04 \text{ mV/}^\circ\text{C}$

    Step 2: Calculate the maximum temperature. The millivoltmeter has a maximum reading of 10mV. We want to find the temperature ($\theta_{max}$) that corresponds to this 10mV reading, keeping the cold junction at 0°C.

    $E_{max} = k \times (\theta_{max} - 0^\circ\text{C})$

    $10 = 0.04 \times \theta_{max}$

    Step 3: Solve for $\theta_{max}$.

    $\theta_{max} = \frac{10}{0.04}$

    $\theta_{max} = \frac{1000}{4}$

    $\theta_{max} = 250^\circ\text{C}$

    Conclusion

    The arrangement can measure up to a maximum temperature of 250°C. This matches option C.

    Exam Tip

    When dealing with thermocouple problems in JAMB, always check if the cold junction is at 0°C (ice point). If the cold junction were at a different temperature (e.g., room temperature), you would have to account for that in your $\Delta\theta$ calculation. Also, remember that the relationship is linear only within a specific range; for higher temperatures, the relationship becomes non-linear, but for JAMB physics, you can safely assume linearity unless stated otherwise.

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84. 84.

    Ripple in a power supply unit is caused by

    1. A.using an alternating current source
    2. B.forward voltage drop
    3. C.heavy load
    4. D.using a zener diode

    Show answer

    Answer: A. using an alternating current source

    AI explanation

    1. Analyze the question

    The question asks for the primary cause of "ripple" in a power supply unit. In electronics, a power supply unit is designed to convert Alternating Current (AC) from the mains into a steady Direct Current (DC). Ripple refers to the small, unwanted residual periodic variation of the DC voltage within a power supply.

    2. Explain the concept

    • Rectification: To convert AC to DC, we use a rectifier (like a diode bridge). The output of a rectifier is "pulsating DC," which rises and falls with the AC input cycle.
    • Smoothing: To get a steady DC, we use a filter (usually a capacitor). However, the capacitor charges and discharges as the AC input cycles, creating a small "ripple" on the output voltage.
    • The Root Cause: If the input were not an Alternating Current (AC) source, there would be no cycles to rectify and no need for smoothing, meaning there would be no ripple. The ripple is essentially the "leftover" effect of the AC nature of the input source that the smoothing circuit couldn't perfectly eliminate.

    3. Show the solution

    • Option A (Using an alternating current source): Since AC changes direction and magnitude periodically, the rectification process produces a pulsating output. Even after filtering, the residual variation (ripple) exists because the source is AC. This is the fundamental cause.
    • Option B (Forward voltage drop): This refers to the small voltage lost across a diode when it conducts. While it affects the total output voltage, it does not cause the periodic fluctuations known as ripple.
    • Option C (Heavy load): A heavy load increases the current drawn, which can increase the magnitude of the ripple (because the capacitor discharges faster), but the load is not the cause of the ripple itself; the AC source is.
    • Option D (Using a zener diode): A Zener diode is actually used to regulate voltage and reduce ripple. It is a solution to voltage instability, not the cause of ripple.

    4. Identify the answer

    5. Exam Tip

    Think of a power supply like a water tank being filled by a pump that turns on and off. The "ripple" is the slight rise and fall of the water level. The pump (the AC source) is the reason you need the tank (the filter) in the first place, and the fluctuations occur because the pump is not a constant, steady flow.

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85. 85.

    The momentum of a car moving at a constant speed in a circular track

    1. A.can be both positive and negative
    2. B.can be zero depending on its position in the track
    3. C.can be zero depending on its inertia in the track
    4. D.a centrifugal

    Show answer

    Answer: A. can be both positive and negative

    AI explanation

    Analysis of the Question

    The question asks about the nature of the momentum of a car moving at a constant speed along a circular track. To answer this, we must look at the definition of momentum and how it behaves in circular motion.

    Concept Explanation

    1. Definition of Momentum ($p$): Momentum is a vector quantity defined as the product of mass ($m$) and velocity ($v$): $$p = m \times v$$
    2. Vector Nature: Because velocity is a vector (it has both magnitude and direction), momentum is also a vector. This means that for momentum to remain constant, both the speed and the direction of the object must remain constant.
    3. Circular Motion: When a car moves in a circular track, even if its speed is constant, its direction is constantly changing at every point along the circle.
    4. Directional Change: Since the direction changes, the velocity vector changes. Consequently, the momentum vector changes continuously as the car moves around the track. Because the direction is constantly shifting, the momentum can point in any direction (positive, negative, or any angle in between) relative to a fixed coordinate system.

    Step-by-Step Solution

    • Step 1: Recognize that momentum is a vector quantity ($\vec{p} = m\vec{v}$).
    • Step 2: In a circular path, the velocity vector is always tangent to the circle. As the car moves, the tangent points in different directions.
    • Step 3: Because the direction of the velocity vector changes, the direction of the momentum vector changes.
    • Step 4: If we define a coordinate system (e.g., an x-axis), the momentum component along that axis will change from positive to negative as the car completes its orbit. Therefore, the momentum can be described as having both positive and negative values depending on the car's position and the chosen reference frame.

    Evaluation of Options

    • Option A: Correct. Since the direction of the momentum vector changes continuously, its components along any fixed axis will fluctuate between positive and negative values.
    • Option B: Incorrect. Momentum is $p = mv$. Since the car has mass and is moving (speed > 0), the magnitude of momentum ($p = mv$) can never be zero.
    • Option C: Incorrect. Inertia is related to mass, and as long as the car has mass and speed, momentum exists.
    • Option D: Incorrect. "Centrifugal" is a force, not a description of momentum.

    Exam Tip

    Always remember the difference between speed (a scalar) and velocity (a vector). In circular motion, speed is constant, but velocity is never constant because the direction is always changing. Since momentum depends on velocity, it is also never constant in circular motion!

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86. 86.

    "Sum of all forces acting on a body is zero." This condition represents equilibrium'

    1. A.First condition
    2. B.Second condition
    3. C.Third condition
    4. D.Fourth condition

    Show answer

    Answer: A. First condition

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87. 87.

    The volume of 0.354g of helium at 273°C and 114cmhg of mercury pressure is 2667cm$^3$. Calculate the volume at STP.

    1. A.2000.25 cm$^3$
    2. B.200.025 cm$^3$
    3. C.4003.27 cm$^3$
    4. D.2010.25 cm$^3$

    Show answer

    Answer: A. 2000.25 cm$^3$

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88. 88.

    The lead-acid accumulator consists of

    1. A.lead as the positive electrode
    2. B.lead acid as the negative electrode
    3. C.hydrochloric acid as the electrolyte
    4. D.tetraoxosulphate (vi) acid as the electrolyte

    Show answer

    Answer: D. tetraoxosulphate (vi) acid as the electrolyte

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89. 89.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.

90. 90.

    Electrons were discovered by

    1. A.Dalton
    2. B.James Charwick
    3. C.J.J. Thompson
    4. D.Niels Bohr

    Show answer

    Answer: C. J.J. Thompson

    AI explanation

    Analysis

    The question asks for the scientist credited with the discovery of the electron, a fundamental subatomic particle.

    Concept

    In the history of atomic physics, several scientists contributed to our understanding of the atom. To identify the correct answer, we must look at the specific discovery associated with each scientist:

    • John Dalton: Proposed the Atomic Theory, suggesting that atoms are indivisible spheres.
    • James Chadwick: Discovered the neutron in 1932.
    • J.J. Thomson: Conducted experiments with cathode ray tubes in 1897. He observed that cathode rays were composed of negatively charged particles, which he named "corpuscles" (later known as electrons).
    • Niels Bohr: Proposed the Bohr model of the atom, which describes electrons orbiting the nucleus in specific energy levels (shells).

    Solution

    1. Evaluate Dalton: Dalton's model viewed the atom as a solid, indivisible sphere. He did not discover subatomic particles.
    2. Evaluate Chadwick: Chadwick is famous for discovering the neutral particle in the nucleus, the neutron.
    3. Evaluate Thomson: Through his cathode ray experiment, Thomson demonstrated that atoms contain smaller, negatively charged particles. This discovery fundamentally changed the view that the atom was indivisible.
    4. Evaluate Bohr: Bohr built upon the work of others to explain the arrangement of electrons, but he did not discover the electron itself.

    Based on historical scientific records, J.J. Thomson is the physicist who discovered the electron.

    Conclusion

    The correct option is C.

    Exam Tip

    To remember these easily for your JAMB exam, use this simple mnemonic:

    • Proton = Rutherford (Gold foil experiment)
    • Electron = Thomson (Cathode ray experiment)
    • Neutron = Chadwick (Beryllium bombardment) Think: "PET-RC" (Proton-E, Thomson-Electron, Rutherford-Chadwick). Wait, actually, just remember "J.J. Thomson = Electrons" as a core fact, as it is a very common JAMB question!

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91. 91.

    A boy pushes a 500kg box along a floor with a force of 2000N. If the velocity of the box is uniform, the co-efficient of friction between the box and the floor is

    1. A.1
    2. B.0.8
    3. C.0.65
    4. D.0.4

    Show answer

    Answer: D. 0.4

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92. 92.

    An a.c of 1A at a frequency of 800 cycles per second flows through a coil, the inductance of which is 2.5mH and the resistance of which is 5Ω. What is the power absorbed in the Coil?

    1. A.5W
    2. B.6W
    3. C.7W
    4. D.8W

    Show answer

    Answer: A. 5W

    AI explanation

    1. Analyze the Question

    We are given:

    • Current ($I$) = $1\text{ A}$
    • Frequency ($f$) = $800\text{ Hz}$
    • Inductance ($L$) = $2.5\text{ mH} = 2.5 \times 10^{-3}\text{ H}$
    • Resistance ($R$) = $5\text{ }\Omega$
    • We need to find the power absorbed in the coil.

    2. Explain the Concept

    In an A.C. circuit containing both a resistor and an inductor (an RL circuit), the power is only dissipated by the resistive component. Inductors store energy in a magnetic field and return it to the circuit; they do not consume power.

    The formula for power ($P$) in an A.C. circuit is:

    $P = I^2R$

    Where:

    • $I$ is the root-mean-square (r.m.s) current.
    • $R$ is the resistance of the coil.

    Note: The inductance and frequency are provided to calculate the inductive reactance ($X_L = 2\pi fL$), but since the question asks for the power absorbed by the coil, we only consider the ohmic resistance.

    3. Show the Solution

    Using the power formula:

    $P = I^2 \times R$

    Substitute the given values:

    $P = (1)^2 \times 5$

    $P = 1 \times 5$

    $P = 5\text{ W}$

    The inductive reactance ($X_L = 2\pi fL$) would be $2 \times 3.142 \times 800 \times 0.0025 \approx 12.57\text{ }\Omega$, but this value is irrelevant to the calculation of real power absorbed, as real power is only consumed by the resistance.

    4. Identify the Answer

    The power absorbed is $5\text{ W}$, which corresponds to option A.

    5. Exam Tip

    In physics problems, examiners often include extra data (like frequency and inductance) to test if you truly understand which components of a circuit consume power. Always remember: Power is only dissipated by resistors. Inductors and capacitors do not consume real power in an ideal circuit.

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93. 93.

    A body moves in SHM between two point 20m on the straight line Joining the points. If the angular speed of the body is 5 rad/s. Calculate its speed when it is 6m from the center of the motion.

    1. A.20 m/s
    2. B.30 m/s
    3. C.40 m/s
    4. D.50 m/s

    Show answer

    Answer: C. 40 m/s

    AI explanation

    1. Analyze the Question

    We are given:

    • The total path length (distance between the two extreme points) = 20 m.
    • Angular speed ($\omega$) = 5 rad/s.
    • Displacement from the center ($x$) = 6 m.
    • We need to find the velocity ($v$) of the body at that specific displacement.

    2. Explain the Concept

    In Simple Harmonic Motion (SHM), the velocity $v$ of a body at any displacement $x$ from the equilibrium position (center) is given by the formula:

    $v = \omega \sqrt{A^2 - x^2}$

    Where:

    • $\omega$ is the angular speed.
    • $A$ is the amplitude (the maximum displacement from the center).
    • $x$ is the instantaneous displacement from the center.

    Note: The amplitude ($A$) is half of the total path length because the body oscillates between $+A$ and $-A$.

    3. Show the Solution

    Step 1: Determine the amplitude ($A$). The body moves between two points 20 m apart. The distance from the center to either extreme point is the amplitude.

    $A = \frac{\text{Total path length}}{2} = \frac{20\text{ m}}{2} = 10\text{ m}$

    Step 2: Substitute the values into the velocity formula.

    • $\omega = 5\text{ rad/s}$
    • $A = 10\text{ m}$
    • $x = 6\text{ m}$

    $v = 5 \sqrt{10^2 - 6^2}$

    $v = 5 \sqrt{100 - 36}$

    $v = 5 \sqrt{64}$

    $v = 5 \times 8$

    $v = 40\text{ m/s}$

    4. Identify the Answer

    Comparing our result to the given options: A. 20 m/s B. 30 m/s C. 40 m/s D. 50 m/s

    The calculated value matches option C.

    5. Exam Tip

    Always remember that in SHM problems, the "distance between the two points" is the path length, which is $2A$. Students often mistake this for the amplitude ($A$) itself. Always divide by 2 before plugging it into your formula!

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94. 94.

    Calculate the velocity ratio of a screw jack of pitch 0.2cm if the length of the tommy bar is 23cm

    1. A.230$\pi$
    2. B.23$\pi$
    3. C.70$\pi$
    4. D.140$\pi$

    Show answer

    Answer: A. 230$\pi$

    AI explanation

    1. Analyze the question

    We are asked to find the Velocity Ratio (V.R.) of a screw jack.

    • Pitch ($p$): 0.2 cm
    • Length of the tommy bar ($R$): 23 cm

    2. Explain the concept

    A screw jack is a simple machine. The velocity ratio of a screw jack is defined as the ratio of the distance moved by the effort (in one complete revolution) to the distance moved by the load (the pitch).

    • In one complete revolution, the effort (applied at the end of the tommy bar) moves in a circle. The distance covered is the circumference of that circle: $2\pi R$.
    • In that same revolution, the load moves forward by a distance equal to the pitch ($p$).

    The formula is:

    $\text{V.R.} = \frac{\text{Distance moved by effort}}{\text{Distance moved by load}} = \frac{2\pi R}{p}$

    3. Show the solution

    • Step 1: Identify the given values. • $R = 23 \text{ cm}$ • $p = 0.2 \text{ cm}$
    • Step 2: Substitute the values into the formula. $$\text{V.R.} = \frac{2 \times \pi \times 23}{0.2}$$
    • Step 3: Simplify the expression. $$\text{V.R.} = \frac{46\pi}{0.2}$$
    • Step 4: Perform the division. To divide by 0.2, you can multiply both the numerator and denominator by 10: $$\text{V.R.} = \frac{460\pi}{2}$$ $$\text{V.R.} = 230\pi$$

    4. Identify the answer

    Comparing our result to the given options, the correct value is $230\pi$. This corresponds to option A.

    5. Tip

    When dealing with screw jacks, always remember that the "effort distance" is the circumference of the circle traced by the handle ($2\pi R$). If the question gives you the diameter of the tommy bar instead of the length (radius), remember to divide the diameter by 2 before using it in the formula!

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95. 95.

    The distance between an object and its real image in a convex lens is 40cm. If the magnification of the image is 3, calculate the focal length of the lens

    1. A.6.5 cm
    2. B.7.5 cm
    3. C.8.5 cm
    4. D.4.5 cm

    Show answer

    Answer: B. 7.5 cm

    AI explanation

    Analysis

    We are given:

    • The total distance between the object ($u$) and the real image ($v$) is $u + v = 40\text{ cm}$.
    • The magnification ($m$) is $3$.
    • We need to find the focal length ($f$).

    Concept

    1. Magnification formula: $m = \frac{v}{u}$. Since $m = 3$, we have $\frac{v}{u} = 3$, which means $v = 3u$.
    2. Lens formula: $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$.

    Step-by-Step Solution

    Step 1: Find the values of $u$ and $v$. We know $u + v = 40$. Substitute $v = 3u$ into the equation: $u + 3u = 40$ $4u = 40$ $u = 10\text{ cm}$

    Now, find $v$: $v = 3u = 3(10) = 30\text{ cm}$

    Step 2: Calculate the focal length ($f$) using the lens formula. $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$ $\frac{1}{f} = \frac{1}{10} + \frac{1}{30}$

    To add these fractions, find the common denominator (which is 30): $\frac{1}{f} = \frac{3 + 1}{30}$ $\frac{1}{f} = \frac{4}{30}$

    Step 3: Solve for $f$. $f = \frac{30}{4}$ $f = 7.5\text{ cm}$

    Conclusion

    The focal length of the lens is 7.5 cm.

    Exam Tip

    When dealing with real images in convex lenses, remember that magnification $m$ is always positive. If the question had mentioned a virtual image, the magnification would be treated as negative ($m = -3$), which would change your calculation for $v$. Always check if the image is real or virtual before starting your calculation!

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96. 96.

    Neutrons were discovered by

    1. A.Faraday
    2. B.Dalton
    3. C.James Chadwick
    4. D.Rutherford

    Show answer

    Answer: C. James Chadwick

    AI explanation

    Analysis

    The question asks for the scientist credited with the discovery of the neutron, a subatomic particle found in the nucleus of an atom.

    Concept Explanation

    To answer this, we look at the history of atomic structure:

    • John Dalton: Proposed the atomic theory, suggesting atoms are indivisible spheres.
    • Michael Faraday: Known for his work on electromagnetism and electrolysis, not subatomic particle discovery.
    • Ernest Rutherford: Discovered the nucleus of the atom through his famous gold foil experiment.
    • James Chadwick: In 1932, he performed experiments bombarding beryllium with alpha particles. He observed that the radiation produced was not affected by electric or magnetic fields, proving it consisted of neutral particles with a mass similar to that of a proton. He named these particles neutrons.

    Step-by-Step Solution

    1. Evaluate Option A (Faraday): Incorrect. His work focused on electricity and magnetism.
    2. Evaluate Option B (Dalton): Incorrect. He proposed the existence of atoms but did not identify subatomic particles.
    3. Evaluate Option C (James Chadwick): Correct. His experimental evidence in 1932 confirmed the existence of the neutron.
    4. Evaluate Option D (Rutherford): Incorrect. While he discovered the nucleus and the proton, he did not discover the neutron.

    Exam Tip

    To remember this for your JAMB exam, use the mnemonic "Chadwick had a neutron". Also, remember the "big three" of atomic discovery:

    • J.J. Thomson: Electron
    • Ernest Rutherford: Proton (and the Nucleus)
    • James Chadwick: Neutron

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97. 97.

    Which of the following is consistent with Charles' law?

    1. A.I
    2. B.II
    3. C.III
    4. D.IV

    Show answer

    Answer: A. I

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98. 98.

    In which of the points labelled A, B, C, D and E on the conductor shown would electric charge tend to concentrate most

    1. A.A
    2. B.B
    3. C.C
    4. D.E

    Show answer

    Answer: B. B

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99. 99.

    If a body moves with a constant speed and at the same time undergoes an acceleration, its motion is said to be

    1. A.oscillation
    2. B.circular
    3. C.rotational
    4. D.rectilinear

    Show answer

    Answer: B. circular

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100. 100.

     Any line or section taken through an advancing wave in which all the particles are in the same phase is called the

     1. A.wavelength
     2. B.wave coast
     3. C.wave trough
     4. D.wave front

     Show answer

     Answer: D. wave front

     AI explanation

     Analysis

     The question asks for the specific term used to describe a line or section of an advancing wave where every particle is vibrating in the same phase (i.e., they are at the same point in their cycle of motion).

     Concept Explanation

     In wave motion, we often visualize waves as moving surfaces. A wavefront is defined as the locus of all points that are in the same phase of vibration.

     • If you imagine a stone dropped into a calm pond, the ripples move outward in circles. Each circle represents a line where all water particles are at the same height (crest or trough) at the same time. These circles are wavefronts.
     • The distance between two consecutive wavefronts is equal to one wavelength.
     • The direction of wave propagation is always perpendicular to the wavefront.

     Step-by-Step Solution

     1. Evaluate Option A (Wavelength): This is the distance between two successive crests or troughs. It is a measurement of length, not a "line or section" of particles.
     2. Evaluate Option B (Wave coast): This is not a standard term used in physics to describe wave motion.
     3. Evaluate Option C (Wave trough): This refers specifically to the lowest point of a wave, not the entire line of particles in the same phase.
     4. Evaluate Option D (Wave front): By definition, a wavefront is the line or surface joining all points that are in the same phase. This matches the description provided in the question perfectly.

     Conclusion

     The correct term for a line or section through an advancing wave where all particles are in the same phase is the wave front.

     Exam Tip

     Think of a wavefront as the "front line" of the wave. Just as soldiers in a line march together at the same pace, all particles on a wavefront move in perfect synchronization (the same phase).

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101. 101.This question needs a diagram, table or passage that we don't have yet, so it isn't shown.