2018 JAMB Physics Past Questions — Part 2

Questions 45–87

45. 45.

    If the fraction of the atoms of a radioactive material left after 120years is $\frac{1}{64}$, what is the half-life of the material?  $\frac{1}{64}$

    1. A.20 years
    2. B.10 years
    3. C.2 years
    4. D.24 years

    Show answer

    Answer: A. 20 years

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46. 46.

    The linear expansivity of brass is 2 x 10$^{-5}$ C$^{-1}$. If the volume of a piece of brass is 15.00cm at 0°C, what is the volume at 100°C

    1. A.16.03cm$^3$
    2. B.15.09cm$^3$
    3. C.16.00cm$^3$
    4. D.15.03cm$^3$

    Show answer

    Answer: B. 15.09cm$^3$

    AI explanation

    1. Analyze the Question

    We are given the linear expansivity ($\alpha$) of brass and its initial volume ($V_0$) at an initial temperature ($\theta_1$). We need to find the final volume ($V_2$) after the temperature increases to $\theta_2$.

    Given data:

    • Linear expansivity ($\alpha$) = $2 \times 10^{-5} \, ^\circ\text{C}^{-1}$
    • Initial volume ($V_0$) = $15.00 \, \text{cm}^3$
    • Initial temperature ($\theta_1$) = $0 \, ^\circ\text{C}$
    • Final temperature ($\theta_2$) = $100 \, ^\circ\text{C}$
    • Change in temperature ($\Delta\theta$) = $100 - 0 = 100 \, ^\circ\text{C}$

    2. Explain the Concept

    When a solid is heated, it expands in all directions. The relationship between linear expansivity ($\alpha$) and cubic (volume) expansivity ($\gamma$) is given by:

    $\gamma = 3\alpha$

    The formula for the change in volume ($\Delta V$) is:

    $\Delta V = V_0 \gamma \Delta\theta$

    Therefore, the final volume ($V_2$) is:

    $V_2 = V_0(1 + \gamma\Delta\theta)$

    3. Show the Solution

    Step 1: Calculate the cubic expansivity ($\gamma$)

    $\gamma = 3 \times \alpha$

    $\gamma = 3 \times (2 \times 10^{-5}) = 6 \times 10^{-5} \, ^\circ\text{C}^{-1}$

    Step 2: Calculate the change in volume ($\Delta V$)

    $\Delta V = V_0 \times \gamma \times \Delta\theta$

    $\Delta V = 15.00 \times (6 \times 10^{-5}) \times 100$

    $\Delta V = 15.00 \times 6 \times 10^{-3}$

    $\Delta V = 90 \times 10^{-3} = 0.09 \, \text{cm}^3$

    Step 3: Calculate the final volume ($V_2$)

    $V_2 = V_0 + \Delta V$

    $V_2 = 15.00 + 0.09 = 15.09 \, \text{cm}^3$

    4. Identify the Answer

    Comparing our result ($15.09 \, \text{cm}^3$) to the given options, it matches option B.

    5. Exam Tip

    Always remember the "3" in $\gamma = 3\alpha$. A common mistake students make is using the linear expansivity directly in the volume formula. Since volume is three-dimensional (length × breadth × height), you must multiply the linear expansivity by 3 to get the volume expansivity.

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47. 47.

    If the focal length of a camera is 20cm, the distance from the film at which the lens must be set to produce a sharp image of 100cm away is

    1. A.17cm
    2. B.20cm
    3. C.25cm
    4. D.100cm

    Show answer

    Answer: C. 25cm

    AI explanation

    Analysis

    To solve this problem, we need to apply the Lens Formula, which relates the focal length ($f$), the object distance ($u$), and the image distance ($v$). In a camera, the "film" acts as the screen where the image is formed.

    Concept

    The lens formula is given by:

    $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

    Where:

    • $f$ = focal length of the lens
    • $u$ = distance of the object from the lens
    • $v$ = distance of the image (the film) from the lens

    Step-by-Step Solution

    1. Identify the given values: • Focal length ($f$) = $20\text{ cm}$ • Object distance ($u$) = $100\text{ cm}$ • Image distance ($v$) = ?

    2. Rearrange the formula to solve for $v$: $$\frac{1}{v} = \frac{1}{f} - \frac{1}{u}$$

    3. Substitute the values into the equation: $$\frac{1}{v} = \frac{1}{20} - \frac{1}{100}$$

    4. Find a common denominator (which is 100): $$\frac{1}{v} = \frac{5}{100} - \frac{1}{100}$$ $$\frac{1}{v} = \frac{4}{100}$$

    5. Solve for $v$: $$\frac{1}{v} = \frac{1}{25}$$ $$v = 25\text{ cm}$$

    The lens must be set at a distance of $25\text{ cm}$ from the film to produce a sharp image.

    Conclusion

    Comparing our result to the options provided, the correct choice is C.

    Exam Tip

    When dealing with lens and mirror problems, always remember the sign convention:

    • Real images (like those formed on a camera film) have a positive image distance ($v$).
    • Virtual images have a negative image distance ($v$).
    • If you ever get a negative result for $v$ in a calculation where you expected a real image, double-check your arithmetic!

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48. 48.

    The time rate of loss of heat by a body is proportional to the

    1. A.temperature of its surroundings
    2. B.temperature of the body
    3. C.difference in temperature between the body and its surroundings
    4. D.ratio of the temperature of the body to that of its surroundings

    Show answer

    Answer: C. difference in temperature between the body and its surroundings

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49. 49.

    A beam of light is incident from air to water at an angle of 30$^o$. Find the angle of refraction if the refractive index of water is 4/3

    1. A.15$^o$
    2. B.18$^o$
    3. C.22$^o$
    4. D.24$^o$

    Show answer

    Answer: C. 22$^o$

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50. 50.

    A man hears his echo from a nearby hill 2s after he shouted. If the frequency of his voice is 260Hz and the wavelength is 1.29m, how far away is the hill?

    1. A.330.0m
    2. B.335.4m
    3. C.660.0m
    4. D.670.8m

    Show answer

    Answer: B. 335.4m

    AI explanation

    1. Analyze the question

    We are given:

    • Time taken for the echo to return ($t$) = 2 seconds
    • Frequency of the sound ($f$) = 260 Hz
    • Wavelength of the sound ($\lambda$) = 1.29 m
    • We need to find the distance ($d$) of the hill from the man.

    2. Explain the concept

    • Wave Equation: The speed of sound ($v$) is calculated using the formula $v = f \times \lambda$.
    • Echo Principle: An echo occurs when sound travels to an obstacle and reflects back. Therefore, the total distance covered by the sound is $2d$ (distance to the hill and back).
    • Speed Formula: Since speed is distance over time ($v = \frac{\text{total distance}}{\text{time}}$), the formula for an echo is $v = \frac{2d}{t}$. Rearranging this to find the distance to the hill: $d = \frac{v \times t}{2}$.

    3. Show the solution

    Step 1: Calculate the speed of sound ($v$)

    $v = f \times \lambda$

    $v = 260 \, \text{Hz} \times 1.29 \, \text{m}$

    $v = 335.4 \, \text{m/s}$

    Step 2: Calculate the distance to the hill ($d$) Using the echo formula $d = \frac{v \times t}{2}$:

    $d = \frac{335.4 \, \text{m/s} \times 2 \, \text{s}}{2}$

    The "2" in the numerator and denominator cancel out:

    $d = 335.4 \, \text{m}$

    4. Identify the answer

    Comparing our result to the given options: A. 330.0m B. 335.4m C. 660.0m D. 670.8m

    The calculated value matches Option B.

    5. Tip

    Always remember that for echoes, the sound travels the distance twice. A common mistake students make is forgetting to divide by 2, which would lead you to choose 670.8m (Option D). Always double-check if the question asks for the "total distance traveled" or the "distance to the obstacle."

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51. 51.

    One of the features of the fission process is that

    1. A.it leads to chain reaction
    2. B.its products are not radioactive
    3. C.neutrons are not released
    4. D.the of the masses of the reactants equals the sum of the masses of the products

    Show answer

    Answer: A. it leads to chain reaction

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52. 52.

    A ball of mass 800g moving horizontally with a speed of 5m/s hits a vertical wall and rebounds with the same speed. The impulse experienced by the ball is?

    1. A.0kgm
    2. B.2kgm/s
    3. C.4kgm/s
    4. D.8kgm/s

    Show answer

    Answer: D. 8kgm/s

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53. 53.

    The energy needed to move a unit positive charge around a complete electric circuit is called the

    1. A.electromotive force
    2. B.electric potential difference
    3. C.electric energy
    4. D.kinetic energy

    Show answer

    Answer: A. electromotive force

    AI explanation

    Analysis

    The question asks for the specific term used to describe the total energy required to move a unit positive charge through an entire electric circuit (including the internal resistance of the source).

    Concept Explanation

    In physics, we distinguish between two similar terms:

    1. Potential Difference (p.d.): This is the work done in moving a unit charge between two specific points in a circuit.
    2. Electromotive Force (e.m.f.): This is the total energy supplied by a source (like a battery or cell) to drive a unit charge around the complete circuit.

    Think of the e.m.f. as the "push" the battery gives to the charge to complete the full loop, whereas potential difference is the "drop" in energy as the charge passes through a specific component (like a resistor or bulb).

    Step-by-Step Solution

    1. Identify the definition: The key phrase here is "around a complete electric circuit."
    2. Evaluate the options: • Electric potential difference refers to the energy change between two points, not the whole circuit. • Electric energy is a general term for the capacity to do work, not the specific definition of the source's driving force. • Kinetic energy relates to the motion of particles, not the electrical potential energy provided by a source. • Electromotive force (e.m.f.) is defined precisely as the energy per unit charge for the entire circuit.
    3. Conclusion: Since the question specifies the energy to move a charge around the complete circuit, it refers to the e.m.f.

    Exam Tip

    A simple way to remember this is: e.m.f. is for the Entire circuit, while p.d. is for a Part of the circuit.

    The correct option is A.

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54. 54.

    A body of mass 100g moving with a velocity of 10$ms^{-1}$ collides with a wall. If after collision it moves with a velocity of 2.0ms−1 in the opposite direction, calculate the change in momentum.

    1. A.0.8Ns
    2. B.1.2Ns
    3. C.12.0Ns
    4. D.80.0Ns

    Show answer

    Answer: B. 1.2Ns

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55. 55.

    A resistor connected to a 12V battery draws a current of 2A. The energy dispatched in the resistor in 5 minutes is ___.

    1. A.3,600J
    2. B.6,000J
    3. C.7,200J
    4. D.14,400J

    Show answer

    Answer: C. 7,200J

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56. 56.

    In homes, electrical appliances and lamps are connected in parallel because

    1. A.less current will be used
    2. B.less voltage will be used
    3. C.parallel connection does not heat up the wires
    4. D.series connection uses high voltage

    Show answer

    Answer: C. parallel connection does not heat up the wires

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57. 57.

    A 20kg mass is to be pulled up a slope inclined at 30° to the horizontal. If efficiency of the plane is 75%. The force required to pull the load up the plane is J [g=10ms$^{− 2}$]

    1. A.87N
    2. B.73.5N
    3. C.133.3N
    4. D.533.2N

    Show answer

    Answer: C. 133.3N

    AI explanation

    1. Analyze the question

    We are given:

    • Mass ($m$) = 20 kg
    • Angle of inclination ($\theta$) = 30°
    • Efficiency ($\eta$) = 75% = 0.75
    • Acceleration due to gravity ($g$) = 10 m/s²
    • We need to find the Effort ($E$) required to pull the load up the plane.

    2. Explain the concept

    In an inclined plane, the Work Input is the work done by the effort ($E \times d$), and the Work Output is the work done against gravity to lift the load ($mgh$).

    • Efficiency ($\eta$) is defined as: $\text{Efficiency} = \frac{\text{Work Output}}{\text{Work Input}} \times 100\%$
    • Work Output = $m \times g \times h$
    • Work Input = $E \times L$ (where $L$ is the length of the slope)
    • From trigonometry, $\sin \theta = \frac{h}{L}$, which means $h = L \sin \theta$.

    Substituting these into the efficiency formula: $\eta = \frac{mgh}{EL} = \frac{mg(L \sin \theta)}{EL} = \frac{mg \sin \theta}{E}$

    Therefore, the formula to find the effort ($E$) is: $E = \frac{mg \sin \theta}{\eta}$

    3. Show the solution

    • Step 1: Calculate the Load ($mg \sin \theta$) Load = $20 \text{ kg} \times 10 \text{ m/s}^2 \times \sin(30^\circ)$ Load = $200 \times 0.5$ Load = $100 \text{ N}$

    • Step 2: Calculate the Effort ($E$) using efficiency $E = \frac{\text{Load}}{\text{Efficiency}}$ $E = \frac{100}{0.75}$ $E = \frac{100}{3/4}$ $E = 100 \times \frac{4}{3}$ $E = \frac{400}{3}$ $E = 133.33 \text{ N}$

    4. Identify the answer

    Comparing our result to the options provided, the correct value is 133.3N. This matches option C.

    5. Tip

    When dealing with inclined planes, always remember that the "Load" is the component of weight acting down the slope ($mg \sin \theta$). If the machine were 100% efficient, the effort would simply equal the load. Since the efficiency is less than 100%, you must always apply more force than the load, which is why we divide the load by the efficiency (a decimal less than 1).

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58. 58.

    A room is heated by means of a charcoal fire, an occupants of the room standing away from the fire is warmed mainly by

    1. A.Convection
    2. B.Radiation
    3. C.Conduction
    4. D.Reflection

    Show answer

    Answer: B. Radiation

    AI explanation

    Analysis

    The question asks for the primary method by which heat is transferred from a charcoal fire to a person standing at a distance in a room. We need to distinguish between the three main modes of heat transfer: conduction, convection, and radiation.

    Concept Explanation

    • Conduction: This is the transfer of heat through direct contact between particles of a solid. It requires a medium and physical touch (e.g., touching a hot metal spoon).
    • Convection: This is the transfer of heat through the actual movement of fluid particles (liquids or gases). Warm air rises and cool air sinks, creating convection currents. While this warms the air in the room, it is not the primary way a person feels the "direct" heat from a fire source at a distance.
    • Radiation: This is the transfer of heat in the form of electromagnetic waves (specifically infrared radiation). Unlike conduction and convection, radiation does not require a material medium to travel. It can pass through a vacuum or air, which is why you can feel the warmth of a fire or the sun even when you are not touching the source or standing directly in the path of rising hot air.

    Step-by-Step Solution

    1. Identify the source: The charcoal fire emits heat energy.
    2. Evaluate the distance: Because the occupant is standing away from the fire, heat cannot reach them through conduction (no physical contact).
    3. Evaluate the medium: While convection currents circulate warm air throughout the room, the "instant" or "direct" warmth felt from a fire source at a distance is primarily due to infrared rays traveling through the air.
    4. Conclusion: Heat transfer by electromagnetic waves is defined as radiation. This is the most efficient way for heat to travel across an open space to an occupant.

    Answer

    The correct option is B.

    Exam Tip

    Think of the sun: it warms the Earth through the vacuum of space where there are no particles for conduction or convection to occur. Whenever you see a question about heat transfer across a distance or through empty space, the answer is almost always Radiation.

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59. 59.

    Convex mirrors are used as driving mirrors because images formed are

    1. A.erect, Virtual and diminished
    2. B.erect, real and diminished
    3. C.erect, virtual and magnified
    4. D.inverted, virtual and diminished

    Show answer

    Answer: A. erect, Virtual and diminished

    AI explanation

    1. Analyze the question

    The question asks for the specific characteristics of the image formed by a convex mirror when used as a driving (side) mirror. We need to identify whether the image is upright (erect) or upside down (inverted), whether it is real or virtual, and whether it is smaller (diminished) or larger (magnified) than the object.

    2. Explain the concept

    • Convex Mirror: This is a spherical mirror where the reflecting surface bulges towards the source of light. It is often called a "diverging mirror."
    • Image Formation: For any position of a real object in front of a convex mirror, the light rays appear to diverge from a point behind the mirror.
    • Characteristics: • Erect: The image is always upright. • Virtual: The image cannot be caught on a screen because it is formed by the apparent intersection of light rays behind the mirror. • Diminished: The image is always smaller than the actual object. This is the primary reason they are used as driving mirrors—they provide a wider field of view, allowing the driver to see more of the road behind them.

    3. Show the solution

    • Step 1: Evaluate the nature of the image. Since convex mirrors always form images behind the mirror, the image is virtual.
    • Step 2: Evaluate the orientation. The image is always upright, meaning it is erect.
    • Step 3: Evaluate the size. Because the rays diverge, the image formed is always smaller than the object, meaning it is diminished.
    • Step 4: Compare with the options. We are looking for "Erect, Virtual, and Diminished."

    4. Identify the answer

    Comparing our findings with the given options:

    • A. erect, virtual and diminished (Matches our findings)
    • B. erect, real and diminished (Incorrect: convex mirrors do not form real images for real objects)
    • C. erect, virtual and magnified (Incorrect: convex mirrors do not magnify)
    • D. inverted, virtual and diminished (Incorrect: the image is not inverted)

    5. Exam Tip

    To remember this easily, use the mnemonic "C-V-E-D": Convex mirrors are Virtual, Erect, and Diminished. Also, remember that convex mirrors are for "wide-angle" viewing, which is why they are perfect for security mirrors in shops and side mirrors on cars!

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60. 60.

    An object moves in a circular path of radius 0.5m with a speed of 1ms$^{-1}$. What is its angular velocity?

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

    Show answer

    Answer: D. 2rads$^{-1}$

    AI explanation

    1. Analyze the question

    We are given:

    • Radius of the circular path ($r$) = $0.5\text{ m}$
    • Linear speed ($v$) = $1\text{ ms}^{-1}$
    • We need to find the angular velocity ($\omega$).

    2. Explain the concept

    In circular motion, there is a direct relationship between the linear speed ($v$) of an object moving along the circumference and its angular velocity ($\omega$). This relationship is defined by the formula:

    $v = r\omega$

    Where:

    • $v$ is the linear velocity (in $\text{ms}^{-1}$)
    • $r$ is the radius (in $\text{m}$)
    • $\omega$ is the angular velocity (in $\text{rads}^{-1}$)

    To find the angular velocity, we rearrange the formula to:

    $\omega = \frac{v}{r}$

    3. Show the solution

    Using the values provided:

    • $v = 1\text{ ms}^{-1}$
    • $r = 0.5\text{ m}$

    Substitute these into the formula:

    $\omega = \frac{1}{0.5}$

    Since $0.5$ is the same as $\frac{1}{2}$:

    $\omega = \frac{1}{1/2} = 1 \times 2 = 2\text{ rads}^{-1}$

    4. Identify the answer

    Comparing our result to the given options: A. $8\text{ rads}^{-1}$ B. $4\text{ rads}^{-1}$ C. $1\text{ rads}^{-1}$ D. $2\text{ rads}^{-1}$

    The correct option is D.

    5. Tip

    When dealing with circular motion problems, always check your units first. If the radius is in centimeters, convert it to meters before calculating to ensure your answer is in the standard SI unit ($\text{rads}^{-1}$). Also, remember the "V-R-Omega" ($v = r\omega$) mnemonic to quickly recall this relationship during your exam!

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61. 61.

    Which of the following has the lowest internal resistance when new?

    1. A.Leclanche cell
    2. B.Daniell cell
    3. C.Torch battery
    4. D.Accumulator

    Show answer

    Answer: D. Accumulator

    AI explanation

    Analysis

    The question asks us to identify which of the listed electrochemical cells possesses the lowest internal resistance when it is brand new. Internal resistance is the opposition to the flow of current offered by the cells and batteries themselves.

    Concept Explanation

    The internal resistance of a cell depends on its chemical construction, the surface area of the electrodes, and the distance between them.

    • Primary Cells (Leclanche, Daniell, Torch/Dry cells): These are designed for low-drain or intermittent use. They typically have higher internal resistance because they rely on chemical reactions that are not optimized for high-current discharge.
    • Secondary Cells (Accumulators/Lead-Acid batteries): These are designed to deliver high currents (like starting a car engine). To achieve this, they are constructed with large plate surface areas and a highly conductive electrolyte (sulfuric acid), which inherently results in a very low internal resistance.

    Step-by-Step Solution

    1. Leclanche cell: Known for high internal resistance due to the porous pot and the nature of the electrolyte used.
    2. Daniell cell: Also has significant internal resistance due to the porous partition required to separate the two electrolytes.
    3. Torch battery (Dry cell): While convenient, it has a relatively high internal resistance compared to secondary cells, which is why it "runs down" quickly when used in high-drain devices.
    4. Accumulator (Lead-Acid battery): This is a secondary cell. Because it is designed to provide large bursts of energy (high current), its design minimizes internal resistance to prevent energy loss as heat within the battery during discharge.

    Comparing these, the accumulator is specifically engineered to have the lowest internal resistance to facilitate high-current output.

    Conclusion

    The accumulator (lead-acid battery) is the correct choice because its design allows for the rapid flow of ions, which corresponds to low internal resistance.

    Exam Tip: Whenever you see a question comparing primary cells (like Leclanche or Daniell) to secondary cells (like Accumulators) regarding current capacity or internal resistance, always remember that secondary cells are built for high performance and lower resistance.

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

63. 63.

    Water of mass 150g at 60$^o$c is added to 300g of water at 20$^o$c and the mixture is well stirred. Calculate the temperature of the mixture.(neglect heat losses to the surroundings)

    1. A.33$^o$c
    2. B.40$^o$c
    3. C.25$^o$c
    4. D.10$^o$c

    Show answer

    Answer: A. 33$^o$c

    AI explanation

    Analysis

    This is a classic calorimetry problem based on the Principle of Conservation of Energy (specifically, the Principle of Mixtures). The principle states that in an isolated system, the heat lost by the hot body is equal to the heat gained by the cold body.

    Concept

    The formula for heat energy is:

    $Q = mc\Delta\theta$

    Where:

    • $m$ = mass
    • $c$ = specific heat capacity of water (which cancels out since both substances are water)
    • $\Delta\theta$ = change in temperature

    Let $T$ be the final temperature of the mixture.

    • For the hot water: Heat lost = $m_1c(T_1 - T)$
    • For the cold water: Heat gained = $m_2c(T - T_2)$

    Solution

    Given:

    • Mass of hot water ($m_1$) = 150g
    • Initial temperature of hot water ($T_1$) = 60°C
    • Mass of cold water ($m_2$) = 300g
    • Initial temperature of cold water ($T_2$) = 20°C

    Step 1: Set up the equation Heat lost = Heat gained

    $m_1c(T_1 - T) = m_2c(T - T_2)$

    Step 2: Simplify Since $c$ (specific heat capacity of water) is on both sides, it cancels out:

    $150(60 - T) = 300(T - 20)$

    Step 3: Solve for T Divide both sides by 150 to make the calculation easier:

    $1(60 - T) = 2(T - 20)$

    $60 - T = 2T - 40$

    Rearrange the terms:

    $60 + 40 = 2T + T$

    $100 = 3T$

    $T = \frac{100}{3}$

    $T = 33.33... ^\circ\text{C}$

    Rounding to the nearest whole number as provided in the options, we get 33°C.

    Conclusion

    The calculated temperature of the mixture is approximately 33°C, which matches option A.

    Exam Tip

    When mixing two quantities of the same substance, you can use the weighted average formula:

    $T = \frac{(m_1 \times T_1) + (m_2 \times T_2)}{m_1 + m_2}$

    Using this: $T = \frac{(150 \times 60) + (300 \times 20)}{150 + 300} = \frac{9000 + 6000}{450} = \frac{15000}{450} = 33.33^\circ\text{C}$. This is a faster way to solve mixture problems in JAMB!

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64. 64.

    The critical angle for light traveling from a transparent medium to air s measured as 34º. The refractive index of the medium is

    1. A.0.56
    2. B.1.50
    3. C.1.79
    4. D.2.02

    Show answer

    Answer: C. 1.79

    AI explanation

    1. Analyze the question

    We are given the critical angle ($c = 34^\circ$) for light traveling from a medium into air. We need to find the refractive index ($n$) of that medium.

    2. Explain the concept

    The relationship between the refractive index ($n$) of a medium and the critical angle ($c$) is defined by Snell's Law at the point of total internal reflection. When light travels from a denser medium to a rarer medium (like air), the formula is:

    $n = \frac{1}{\sin(c)}$

    Where:

    • $n$ is the refractive index.
    • $c$ is the critical angle.

    3. Show the solution

    • Step 1: Identify the given value: $c = 34^\circ$.
    • Step 2: Plug the value into the formula: $$n = \frac{1}{\sin(34^\circ)}$$
    • Step 3: Calculate the sine of $34^\circ$: Using a calculator, $\sin(34^\circ) \approx 0.5592$.
    • Step 4: Perform the division: $$n = \frac{1}{0.5592}$$ $$n \approx 1.788$$

    Rounding this to two decimal places, we get 1.79.

    4. Identify the answer

    Comparing our result to the given options: A. 0.56 B. 1.50 C. 1.79 D. 2.02

    The calculated value matches option C.

    5. Tip

    When dealing with critical angle problems, always remember that the refractive index $n$ must be greater than 1. If you calculate a value less than 1, you have likely inverted your formula (i.e., you calculated $\sin(c)$ instead of $1/\sin(c)$). Also, ensure your calculator is in Degree mode (DEG) and not Radians (RAD) before calculating trigonometric functions!

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65. 65.

    In a series R-L-C circuit at resonance, the voltages across the resistor and the inductor are 30V and 40V respectively. What is the voltage across the capacitor?

    1. A.30V
    2. B.70V
    3. C.50V
    4. D.40V

    Show answer

    Answer: D. 40V

    AI explanation

    Analysis

    This question tests your understanding of the properties of a series R-L-C circuit at resonance. You are given the voltage across the resistor ($V_R$) and the inductor ($V_L$), and you need to find the voltage across the capacitor ($V_C$).

    Concept

    In a series R-L-C circuit, resonance occurs when the inductive reactance ($X_L$) is equal to the capacitive reactance ($X_C$).

    Mathematically: $X_L = X_C$

    Since the current ($I$) flowing through all components in a series circuit is the same, we can multiply both sides of the equation by $I$: $I \times X_L = I \times X_C$

    This leads to the fundamental condition for resonance in terms of voltage: $V_L = V_C$

    This means that at resonance, the voltage across the inductor is exactly equal in magnitude to the voltage across the capacitor.

    Solution

    1. Identify the given values: • Voltage across the resistor ($V_R$) = 30V • Voltage across the inductor ($V_L$) = 40V

    2. Apply the resonance condition: • At resonance, the inductive voltage and capacitive voltage are equal ($V_L = V_C$). • Since $V_L = 40V$, then $V_C$ must also be 40V.

    Note: The voltage across the resistor ($V_R$) is equal to the total supply voltage of the circuit at resonance, but it does not change the fact that $V_L$ must equal $V_C$.

    Conclusion

    Based on the principle of resonance in R-L-C circuits, the voltage across the capacitor is 40V.

    Exam Tip

    Always remember that at resonance, the circuit behaves as if it were purely resistive. The voltages across the inductor and capacitor are $180^\circ$ out of phase, which is why they "cancel" each other out in the total voltage calculation ($V_{total} = \sqrt{V_R^2 + (V_L - V_C)^2}$). Since $V_L - V_C = 0$, the total voltage is simply $V_R$.

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66. 66.

    A ball of mass 5.0kg hits a smooth vertical wall normally with a speed of 2ms$^{-1}$. Determine the magnitude of the resulting impulse

    1. A.20.0kgms$^{-1}$
    2. B.10.0kgms$^{-1}$
    3. C.5.0kgms$^{-1}$
    4. D.2.5kgms$^{-1}$

    Show answer

    Answer: A. 20.0kgms$^{-1}$

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

68. 68.

    A narrow beam of white light can be split up into different Colours by a glass prism. The correct explanation is that

    1. A.white light Is an electromagnetic wave
    2. B.the prism has all the colours of the white light
    3. C.different colours of white light travel with different speeds in glass
    4. D.white light has undergone total Internal reflection in the prism

    Show answer

    Answer: C. different colours of white light travel with different speeds in glass

    AI explanation

    Analysis

    The question asks for the physical reason why a glass prism splits white light into its constituent colors (a phenomenon known as dispersion).

    Concept Explanation

    White light is composed of a spectrum of colors (Red, Orange, Yellow, Green, Blue, Indigo, Violet). When white light enters a glass prism, it undergoes refraction (bending).

    The key principle here is the Refractive Index ($n$). The refractive index of a material is defined as the ratio of the speed of light in a vacuum ($c$) to the speed of light in that medium ($v$):

    $n = \frac{c}{v}$

    In a glass prism, the speed of light depends on its frequency (or wavelength). Different colors have different frequencies; therefore, they travel at different speeds within the glass. Because they travel at different speeds, each color is refracted (bent) by a different angle. Violet light travels the slowest and bends the most, while red light travels the fastest and bends the least. This separation of speeds is what causes the white light to spread out into a spectrum.

    Step-by-Step Solution

    1. Analyze the options: • A: While true that light is an electromagnetic wave, this property alone does not explain why it splits into colors when passing through a prism. • B: The prism does not "contain" the colors; it merely acts as a medium that separates the colors already present in the white light. • C: Because the refractive index of glass varies with the wavelength of light, each color travels at a different speed ($v = c/n$). This difference in speed causes the different angles of refraction, leading to dispersion. • D: Total internal reflection occurs when light travels from a denser medium to a less dense medium at an angle greater than the critical angle. This is not the mechanism behind the splitting of white light into a spectrum.

    2. Conclusion: The splitting of white light (dispersion) is fundamentally caused by the variation in the speed of different colors of light as they pass through the glass medium.

    Final Answer

    The correct explanation is that different colors of white light travel with different speeds in glass, leading to different degrees of refraction.

    Correct Option: C

    Exam Tip

    Remember the acronym ROYGBIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet). Red has the longest wavelength and travels the fastest in glass (bends the least), while Violet has the shortest wavelength and travels the slowest in glass (bends the most). This relationship is a favorite topic in JAMB Physics!

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69. 69.

    Which of the following statements are TRUE of isotopes? I. Isotopes of an element have the same chemical properties because they have the same number of electrons II. Isotopes of elements are normally separated using physical properties III. Isotopes of an element have the same number of protons in their nuclei

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

    Show answer

    Answer: D. I, II and III

    AI explanation

    To solve this question, let’s break down the definition and characteristics of isotopes.

    1. Analyze the Concept

    Isotopes are atoms of the same element that have the same number of protons (atomic number) but a different number of neutrons (mass number).

    • Statement I: Chemical properties are determined by the arrangement of electrons in the outer shell of an atom. Since isotopes of the same element have the same number of protons, they must have the same number of electrons to remain neutral. Therefore, they exhibit identical chemical properties. (True)
    • Statement II: Because isotopes have different masses (due to the difference in the number of neutrons), they have slightly different physical properties (such as density, rate of diffusion, or boiling point). These differences in physical properties are exactly what scientists exploit to separate them (e.g., using a mass spectrometer or gaseous diffusion). (True)
    • Statement III: By definition, the identity of an element is determined by its proton number. If the number of protons were different, it would be a completely different element. Thus, all isotopes of a specific element must have the same number of protons. (True)

    2. Step-by-Step Evaluation

    • Statement I is correct: Same electrons = same chemical behavior.
    • Statement II is correct: Physical separation methods (like mass spectrometry) rely on the mass difference between isotopes.
    • Statement III is correct: The definition of an isotope requires the proton number to remain constant.

    Since all three statements (I, II, and III) are scientifically accurate, the correct option must include all of them.

    3. Conclusion

    Exam Tip: When you see questions about isotopes, always remember the "P-E-N" rule:

    • Protons: Same
    • Electrons: Same
    • Neutrons: Different This simple mnemonic will help you quickly identify the properties of isotopes in any exam setting.

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70. 70.

    A positively charged rod X is brought near an uncharged metal sphere Y and is then touched by a finger with X still in place. When the finger is removed, the result is that Y has

    1. A.no charge and a zero potential
    2. B.a positive charge and a zero potential
    3. C.a negative charge and a positive potential
    4. D.a negative charge and a negative potential

    Show answer

    Answer: D. a negative charge and a negative potential

    AI explanation

    Analysis of the Question

    This question tests your understanding of electrostatic induction and charging by conduction (earthing). We are looking at what happens to the charge and potential of a neutral metal sphere when it is influenced by a charged rod and then grounded.

    Concept Explanation

    1. Induction: When a positively charged rod (X) is brought near an uncharged metal sphere (Y), the free electrons in the metal sphere are attracted toward the rod. This causes the side of the sphere closest to the rod to become negatively charged, while the side furthest away becomes positively charged.
    2. Earthing (Touching with a finger): When you touch the sphere with your finger, you provide a path for electrons to flow between the Earth and the sphere. Because the positive charge on the far side of the sphere is "repelled" by the positive rod, electrons from the Earth flow into the sphere to neutralize that positive charge.
    3. Result: Once the finger is removed, the sphere is left with an excess of electrons (a negative charge) that were drawn from the Earth.
    4. Potential: The potential of an object is determined by its charge. Since the sphere now has a net negative charge, its electric potential is negative relative to the Earth (which is at zero potential).

    Step-by-Step Solution

    • Step 1: Rod X (positive) is brought near Sphere Y. Electrons in Y move toward X.
    • Step 2: The far side of Y becomes positive.
    • Step 3: Touching Y with a finger allows electrons from the Earth to flow into Y to neutralize the positive side.
    • Step 4: Removing the finger traps these extra electrons on the sphere.
    • Step 5: Sphere Y now has a net negative charge.
    • Step 6: Because the sphere is negatively charged, its potential is negative.

    Conclusion

    The sphere gains a negative charge due to the flow of electrons from the Earth, and consequently, it acquires a negative potential.

    Exam Tip: Remember the "Finger Rule" for induction: When you ground an object near a positive rod, it gains a negative charge. If you ground it near a negative rod, it gains a positive charge. The potential always follows the sign of the net charge on the object.

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71. 71.

    Which of the following phenomena cannot be explained by the molecular theory of matter?

    1. A.Conduction
    2. B.Convection
    3. C.Expansion
    4. D.Radiation

    Show answer

    Answer: D. Radiation

    AI explanation

    Analysis of the Question

    The question asks us to identify which of the listed heat transfer processes cannot be explained by the molecular theory of matter. The molecular theory of matter states that matter is made up of tiny particles (atoms or molecules) that are in constant motion and interact with one another.

    Concept Explanation

    To solve this, let's look at how heat is transferred in each process:

    1. Conduction: Heat is transferred through a material by the vibration and collision of neighboring molecules. This is a direct application of the molecular theory.
    2. Convection: Heat is transferred by the actual movement of fluid (liquid or gas) particles from one place to another. This movement is a result of changes in density caused by molecular kinetic energy. This is also explained by the molecular theory.
    3. Expansion: When a substance is heated, its molecules gain kinetic energy and vibrate more vigorously, pushing each other further apart. This increase in average separation explains why substances expand.
    4. Radiation: This is the transfer of heat in the form of electromagnetic waves (specifically infrared radiation). Unlike conduction and convection, radiation does not require a material medium to travel. It can occur in a vacuum (like heat from the sun reaching the Earth). Because it does not rely on the interaction or movement of matter particles, it is not explained by the molecular theory of matter.

    Step-by-Step Solution

    • Step 1: Evaluate Conduction. It requires a medium (atoms/molecules) to transfer energy. (Explained by molecular theory).
    • Step 2: Evaluate Convection. It requires a medium (fluid) to transfer energy. (Explained by molecular theory).
    • Step 3: Evaluate Expansion. It is a direct result of increased molecular vibration and separation. (Explained by molecular theory).
    • Step 4: Evaluate Radiation. It involves electromagnetic waves that travel through space without needing particles. Therefore, the molecular theory is insufficient to explain how radiation propagates through a vacuum.

    Conclusion

    The phenomenon that cannot be explained by the molecular theory of matter is Radiation.

    Exam Tip

    Whenever you see a question about heat transfer, remember this: Conduction and Convection need "stuff" (matter) to happen, while Radiation is the "loner" that can travel through empty space (a vacuum).

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72. 72.

    The process whereby a liquid turns spontaneously into vapour is called

    1. A.regelation
    2. B.evaporation
    3. C.boiling
    4. D.sublimation

    Show answer

    Answer: B. evaporation

    AI explanation

    1. Analyze the question

    The question asks for the specific term used to describe the spontaneous change of a substance from a liquid state to a gaseous (vapour) state.

    2. Explain the concept

    • Evaporation: This is a surface phenomenon where liquid molecules gain enough kinetic energy to escape into the atmosphere as vapour. It occurs at any temperature below the boiling point and happens spontaneously at the surface of the liquid.
    • Boiling: This is a bulk phenomenon where the entire liquid turns into vapour at a specific temperature called the boiling point. It requires an external heat source to maintain the process.
    • Regelation: This is the phenomenon where ice melts under pressure and refreezes when the pressure is removed.
    • Sublimation: This is the process where a solid changes directly into a gas without passing through the liquid state (e.g., camphor or dry ice).

    3. Show the solution

    • Since the question specifies a spontaneous process where a liquid turns into vapour, we must look for the term that describes a natural, surface-level transition.
    • Boiling is not spontaneous in the same sense because it requires the liquid to reach its specific boiling point through added heat.
    • Evaporation happens naturally at the surface of a liquid at any temperature, making it the correct definition for the process described.

    4. Identify the answer

    Comparing our analysis to the options provided:

    • A. regelation (Incorrect)
    • B. evaporation (Correct)
    • C. boiling (Incorrect - requires specific temperature/heat)
    • D. sublimation (Incorrect - involves solids)

    5. Tip

    To remember the difference: Evaporation happens at the surface and at any temperature (think of a puddle drying up on a sunny day), while Boiling happens throughout the entire liquid and only at a fixed temperature (think of water in a kettle).

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

74. 74.

    Which of the following concepts is not an evidence of the particles nature of matter?

    1. A.Diffusion
    2. B.Brownian motion
    3. C.Diffraction
    4. D.Esterification

    Show answer

    Answer: C. Diffraction

    AI explanation

    Analysis

    The question asks us to identify which of the listed phenomena is not evidence of the particulate nature of matter. To answer this, we need to understand what "particulate nature of matter" means and which physical or chemical processes demonstrate that matter is made of tiny, moving particles.

    Concept Explanation

    The kinetic theory of matter states that all matter is made up of tiny particles that are in constant motion. Evidence for this theory includes:

    1. Brownian Motion: The random, zigzag movement of microscopic particles suspended in a fluid (liquid or gas). This is caused by the collision of invisible, fast-moving fluid molecules with the visible particles.
    2. Diffusion: The net movement of particles from a region of higher concentration to a region of lower concentration. This proves that particles are in constant random motion and can move through spaces between other particles.
    3. Osmosis: A special case of diffusion involving the movement of solvent molecules through a semi-permeable membrane.
    4. Esterification: This is a chemical reaction between an alcohol and an organic acid to form an ester and water. While it involves molecules, it is a chemical reaction (a process of bond breaking and bond formation), not a physical phenomenon used as evidence for the kinetic theory of matter.

    Wait, let's look at the options again:

    • Diffusion (A): Evidence of particle motion.
    • Brownian motion (B): Direct evidence of particle existence and motion.
    • Diffraction (C): This is a property of waves. Diffraction occurs when a wave encounters an obstacle or a slit that is comparable in size to its wavelength. It is a fundamental characteristic of wave motion, not a proof that matter is made of particles.
    • Esterification (D): While chemical, it involves the interaction of molecules.

    However, in the context of physics examinations like JAMB, Diffraction is the classic "odd one out" because it is a phenomenon exclusively associated with wave behavior, whereas the others (Diffusion, Brownian motion) are standard proofs for the particle theory.

    Step-by-Step Solution

    1. Evaluate A (Diffusion): Diffusion occurs because particles are in constant motion. This is evidence of the particle nature of matter.
    2. Evaluate B (Brownian motion): This is the most famous evidence for the kinetic theory of matter, confirming that particles exist and are constantly moving.
    3. Evaluate C (Diffraction): Diffraction is the bending of waves around corners or through apertures. It is a defining characteristic of waves, not particles. Therefore, it does not provide evidence for the particle nature of matter.
    4. Evaluate D (Esterification): Although this is a chemical process, it involves the rearrangement of atoms and molecules, which inherently assumes the existence of particles.

    Comparing these, Diffraction is the most distinct "non-particle" concept here.

    Conclusion

    Diffraction is a wave phenomenon, whereas the other options relate to the behavior of particles.

    Exam Tip

    Whenever you see a question about "evidence of the particulate nature of matter," look for keywords like motion, collision, or mixing. If you see terms like diffraction, interference, or polarization, those are almost always related to wave properties, not particle properties!

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75. 75.

    An electric heating coil rated at 1Kw is used to heat 2kg of water for 2 minutes. The initial water temperature is 30$^o$C. Taking the specific heat of the water as 4,000Jkg $^{-1}$ and neglecting that of the container, the final water temperature is

    1. A.15.0$^o$C
    2. B.45.0$^o$C
    3. C.52.5$^o$C
    4. D.60.0$^o$C

    Show answer

    Answer: B. 45.0$^o$C

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76. 76.

    Musical instruments playing the same note can be distinguished from one another owing to the difference in their

    1. A.quality
    2. B.pitch
    3. C.intensity
    4. D.loudness

    Show answer

    Answer: A. quality

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77. 77.

    The friction which exist between two layers of liquid in relative motion is called.

    1. A.Capillary
    2. B.Surface
    3. C.Viscosity
    4. D.Cohesion

    Show answer

    Answer: C. Viscosity

    AI explanation

    Analysis

    The question asks for the specific term used to describe the internal resistance or "friction" that occurs when different layers of a liquid move past each other at different velocities.

    Concept Explanation

    In physics, fluids (liquids and gases) possess a property that resists the relative motion of their layers. This is essentially the fluid's version of friction.

    • Viscosity is defined as the internal friction of a fluid. When a liquid flows, the layer in contact with a surface moves slower than the layers further away. The force required to maintain this velocity gradient is due to the viscosity of the fluid.
    • Capillarity refers to the ability of a liquid to flow in narrow spaces without the assistance of external forces (like gravity).
    • Surface Tension is the property of a liquid surface that allows it to resist an external force, caused by the attraction of particles in the surface layer.
    • Cohesion is the intermolecular force that holds molecules of the same substance together.

    Step-by-Step Solution

    1. Identify the phenomenon: The question describes "friction between two layers of liquid in relative motion."
    2. Evaluate the options: • A (Capillary) relates to flow in narrow tubes. • B (Surface) is too broad and usually refers to surface tension. • C (Viscosity) is specifically defined as the measure of a fluid's resistance to gradual deformation by shear stress or tensile stress (internal friction). • D (Cohesion) is the force of attraction between molecules, not the friction between moving layers.
    3. Conclusion: Viscosity is the correct physical term for the internal friction of a fluid.

    Correct Answer

    The correct option is C.

    Exam Tip

    Think of viscosity as the "thickness" or "stickiness" of a liquid. Honey has high viscosity (it flows slowly because the layers have high internal friction), while water has low viscosity. Remembering this relationship will help you identify the concept easily in future exams!

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78. 78.

    Which of the following phenomena is the practical evidence for the existence of the continual motion of molecules.

    1. A.Transitional Motion
    2. B.Rotational Motion
    3. C.Brownian Motion
    4. D.Oscillatory Motion

    Show answer

    Answer: C. Brownian Motion

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

80. 80.

    A lens of focal length 15cm forms an erect image which is three times the size of the object. The distance between the object and the image is ___.

    1. A.10cm
    2. B.20cm
    3. C.30cm
    4. D.40cm

    Show answer

    Answer: B. 20cm

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81. 81.

    An object weighs 30N in air and 21N in water. The weight of the object when completely immersed in a liquid of relative density 1.4 is

    1. A.25.2N
    2. B.17.4N
    3. C.12.6N
    4. D.9.0N

    Show answer

    Answer: B. 17.4N

    AI explanation

    1. Analyze the question

    We are given the weight of an object in air and its weight when immersed in water. We need to find its weight when immersed in a different liquid with a known relative density.

    2. Explain the concept

    This problem is based on Archimedes' Principle, which states that the upthrust on an object immersed in a fluid is equal to the weight of the fluid displaced.

    • Upthrust in water = Weight in air - Weight in water
    • Upthrust in any liquid = Weight in air - Weight in liquid
    • Relative Density (RD) = $\frac{\text{Upthrust in liquid}}{\text{Upthrust in water}}$

    3. Show the solution

    Step 1: Calculate the upthrust in water.

    • Weight in air ($W_a$) = 30 N
    • Weight in water ($W_w$) = 21 N
    • Upthrust in water ($U_w$) = $W_a - W_w = 30 - 21 = 9\text{ N}$

    Step 2: Calculate the upthrust in the new liquid. We know the Relative Density (RD) of the liquid is 1.4.

    • $RD = \frac{\text{Upthrust in liquid } (U_l)}{\text{Upthrust in water } (U_w)}$
    • $1.4 = \frac{U_l}{9}$
    • $U_l = 1.4 \times 9 = 12.6\text{ N}$

    Step 3: Calculate the weight of the object in the liquid.

    • Weight in liquid ($W_l$) = Weight in air - Upthrust in liquid
    • $W_l = 30 - 12.6$
    • $W_l = 17.4\text{ N}$

    4. Identify the answer

    Comparing our result to the given options, the correct value is 17.4N.

    5. Tip

    When dealing with buoyancy problems, always remember that Upthrust = Weight in air - Weight in liquid. If you are given the Relative Density of a liquid, it is simply the ratio of the upthrust in that liquid to the upthrust in water. Don't let the "Relative Density" term confuse you—it is just a multiplier for the upthrust!

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82. 82.

    A pulley system has three pulleys in the fixed block and two in the movable block and if the pulley has an efficiency of 72%, the mechanical advantage of the system is?

    1. A.36.0
    2. B.7.2
    3. C.5.0
    4. D.3.6

    Show answer

    Answer: D. 3.6

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83. 83.

    The image of an object is located 6cm behind a convex mirror. If it's magnification is 0.6, calculate the focal length of the mirror

    1. A.3.75cm
    2. B.6.70cm
    3. C.10.00cm
    4. D.-15.00cm

    Show answer

    Answer: D. -15.00cm

    AI explanation

    1. Analyze the question

    • Mirror type: Convex mirror.
    • Image position ($v$): The image is 6cm behind the mirror. For mirrors, images formed behind the mirror are virtual, so $v = -6\text{ cm}$.
    • Magnification ($m$): $0.6$.
    • To find: Focal length ($f$).

    2. Explain the concept

    • Magnification formula: $m = \frac{-v}{u}$, where $v$ is the image distance and $u$ is the object distance.
    • Mirror formula: $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$.
    • Sign Convention: For a convex mirror, the focal length ($f$) is always positive, and the image distance ($v$) for a virtual image is negative.

    3. Show the solution

    Step 1: Find the object distance ($u$) using the magnification formula.

    $m = \frac{-v}{u}$

    $0.6 = \frac{-(-6)}{u}$

    $0.6 = \frac{6}{u}$

    $u = \frac{6}{0.6} = 10\text{ cm}$

    Step 2: Use the mirror formula to find the focal length ($f$).

    $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

    $\frac{1}{f} = \frac{1}{10} + \frac{1}{-6}$

    $\frac{1}{f} = \frac{1}{10} - \frac{1}{6}$

    Find the Least Common Multiple (LCM) of 10 and 6, which is 30:

    $\frac{1}{f} = \frac{3 - 5}{30}$

    $\frac{1}{f} = \frac{-2}{30}$

    $\frac{1}{f} = \frac{-1}{15}$

    $f = -15\text{ cm}$

    4. Identify the answer

    The calculation gives $-15\text{ cm}$. While convex mirrors typically have positive focal lengths in standard optics, the mathematical result based on the provided values leads to $-15\text{ cm}$. This matches option D.

    5. Tip

    Always remember the "Real is Positive, Virtual is Negative" rule for mirror distances. If the question says the image is "behind the mirror," it is virtual, so always assign a negative sign to $v$ immediately. This simple habit prevents most errors in mirror calculations!

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84. 84.

    Which of the following does NOT describe the Image formed by a plane minor?

    1. A.Erect
    2. B.Laterally inverted
    3. C.Same distance from mirror as object
    4. D.Magnified

    Show answer

    Answer: D. Magnified

    AI explanation

    Analysis of the Question

    The question asks us to identify the property that is NOT associated with an image formed by a plane mirror. To answer this, we need to recall the characteristics of images produced by plane mirrors.

    Concept Explanation

    When an object is placed in front of a plane mirror, the image formed follows these specific laws of reflection:

    1. Erect: The image is upright (not upside down).
    2. Virtual: The image cannot be caught on a screen; it appears to be behind the mirror.
    3. Laterally Inverted: The left side of the object appears as the right side of the image (like how your reflection winks with the opposite eye).
    4. Same Size: The image is exactly the same size as the object.
    5. Same Distance: The distance of the image from the mirror is equal to the distance of the object from the mirror.
    6. Magnification: Since the image is the same size as the object, the magnification is exactly 1.

    Step-by-Step Solution

    • Option A (Erect): This is a true characteristic of a plane mirror image.
    • Option B (Laterally inverted): This is a true characteristic (the reason why "AMBULANCE" is written in reverse on vehicles).
    • Option C (Same distance from mirror as object): This is a true characteristic; the image distance ($v$) equals the object distance ($u$).
    • Option D (Magnified): "Magnified" means the image is larger than the object. Since a plane mirror produces an image of the same size (magnification = 1), it cannot produce a magnified image. Therefore, this statement is false.

    Conclusion

    The statement that does NOT describe the image formed by a plane mirror is that it is magnified.

    Exam Tip: Always remember the acronym V-E-L-S for plane mirrors: Virtual, Erect, Laterally inverted, and Same size. If an option mentions "Real" or "Magnified/Diminished," it is definitely incorrect for a plane mirror!

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85. 85.

    Which of the following is the dimension of pressure

    1. A.ML$^{−1}$T$^{−2}$
    2. B.MLT$^{−2}$
    3. C.ML$^{2}$T$^{3}$
    4. D.ML$^{−3}$

    Show answer

    Answer: A. ML$^{−1}$T$^{−2}$

    AI explanation

    1. Analyze the question

    The question asks for the dimensional formula of pressure. To find this, we need to break down pressure into its fundamental physical quantities: Mass ($M$), Length ($L$), and Time ($T$).

    2. Explain the concept

    In physics, dimensions are expressed in terms of the base units of the SI system.

    • Pressure ($P$) is defined as Force ($F$) per unit Area ($A$): $$P = \frac{F}{A}$$
    • Force ($F$) is defined by Newton's Second Law as mass ($m$) times acceleration ($a$): $$F = m \times a$$ • Dimension of mass ($m$) = $[M]$ • Dimension of acceleration ($a$) = $[LT^{-2}]$ • Therefore, dimension of Force = $[MLT^{-2}]$
    • Area ($A$) is length times width (or length squared): • Dimension of Area = $[L^2]$

    3. Show the solution

    Now, substitute the dimensions of Force and Area into the pressure formula:

    $[P] = \frac{[Force]}{[Area]}$

    $[P] = \frac{[MLT^{-2}]}{[L^2]}$

    Using the laws of indices, we subtract the exponent of the denominator from the numerator:

    $[P] = M \times L^{(1-2)} \times T^{-2}$

    $[P] = ML^{-1}T^{-2}$

    4. Identify the answer

    Comparing our result with the given options: A. $ML^{-1}T^{-2}$ B. $MLT^{-2}$ C. $ML^2T^3$ D. $ML^{-3}$

    The correct dimension is $ML^{-1}T^{-2}$, which matches option A.

    5. Tip

    Exam Strategy: If you ever forget the dimension of pressure, remember that pressure is the same as Stress (Force/Area) or Young's Modulus. Also, remember that $MLT^{-2}$ is the standard dimension for Force. Whenever you see "per unit area," simply divide the Force dimension by $L^2$.

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86. 86.

    The photo cell works on the principle of the

    1. A.Voltaic cell
    2. B.Emission of electron by incident radiation
    3. C.Emission of protons by incident radiation
    4. D.Photographic plate

    Show answer

    Answer: B. Emission of electron by incident radiation

    AI explanation

    Analysis

    This question tests your understanding of Photoelectric Effect, a fundamental topic in Modern Physics. You are asked to identify the physical principle that allows a photocell (or photoelectric cell) to function.

    Concept Explanation

    A photocell is a device that converts light energy into electrical energy. It operates based on the Photoelectric Effect.

    The photoelectric effect occurs when light (electromagnetic radiation) of a sufficiently high frequency strikes the surface of a metal. This interaction causes the metal to eject electrons from its surface. These ejected electrons are called photoelectrons. When these electrons flow through a circuit, they create an electric current.

    • Key takeaway: The process involves light (incident radiation) hitting a surface and causing the release (emission) of electrons.

    Step-by-Step Solution

    1. Evaluate Option A: A Voltaic cell (or electrochemical cell) produces electricity through chemical reactions, not light. This is incorrect.
    2. Evaluate Option B: This describes the photoelectric effect perfectly—incident radiation (light) causes the emission of electrons from a material. This is the correct principle.
    3. Evaluate Option C: Protons are located in the nucleus of an atom and are not emitted during the photoelectric effect. This is incorrect.
    4. Evaluate Option D: A photographic plate is used to record images through chemical changes caused by light, not to generate electrical current via electron emission. This is incorrect.

    Conclusion

    The photocell functions because incident light radiation provides enough energy to overcome the work function of the metal surface, resulting in the emission of electrons.

    Exam Tip

    Whenever you see "Photo" in Physics, think Light. Whenever you see "Electric," think Electrons. Therefore, "Photoelectric" simply means using light to move electrons!

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87. 87.

    What type of reaction is represented by the following scheme? $_{1} ^{2} X$ + $_{1} ^{2} Y$  -----> $_{2} ^{3} Z$ + $_{0} ^{1} n$ + energy

    1. A.fusion reaction
    2. B.fission reaction
    3. C.Chain reaction
    4. D.radioactive decay

    Show answer

    Answer: A. fusion reaction

    AI explanation

    Analysis of the Question

    The equation provided is: $_{1} ^{2} X$ + $_{1} ^{2} Y$ $\rightarrow$ $_{2} ^{3} Z$ + $_{0} ^{1} n$ + energy

    We need to identify the type of nuclear reaction occurring here by examining the reactants and the products.

    Concept Explanation

    • Nuclear Fusion: This is a reaction where two light atomic nuclei (usually isotopes of hydrogen, like deuterium or tritium) combine to form a heavier nucleus, releasing a significant amount of energy in the process.
    • Nuclear Fission: This is the opposite of fusion. It occurs when a heavy, unstable nucleus (like Uranium-235) splits into two or more smaller, lighter nuclei, usually triggered by a neutron.
    • Chain Reaction: This is a series of fission reactions where the neutrons released from one fission event trigger further fission events.
    • Radioactive Decay: This is the spontaneous process by which an unstable nucleus loses energy by emitting radiation (alpha, beta, or gamma particles).

    Step-by-Step Solution

    1. Examine the reactants: We have two light nuclei, $_{1} ^{2} X$ and $_{1} ^{2} Y$ (both are isotopes of hydrogen, specifically deuterium).
    2. Examine the products: These two light nuclei combine to form a heavier nucleus, $_{2} ^{3} Z$ (Helium-3), along with a neutron ($_{0} ^{1} n$) and energy.
    3. Compare with definitions: Since two light nuclei are merging to form a heavier nucleus, this is a classic example of nuclear fusion.
    4. Check the balance: • Mass numbers: $2 + 2 = 3 + 1$ (Total = 4 on both sides). • Atomic numbers: $1 + 1 = 2 + 0$ (Total = 2 on both sides). • The equation is balanced, confirming it is a valid nuclear reaction.

    Conclusion

    Because the reaction involves the joining of two light nuclei to form a heavier one, it is classified as a fusion reaction.

    Exam Tip

    A simple way to remember the difference:

    • Fusion = Fusing together (like two small things becoming one big thing).
    • Fission = Fission/Fissure (like a crack or split, where one big thing breaks into smaller things).

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