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. 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:

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:

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.