Particles of mass 10 ^ -2 kg is fixed to the tip of a fan blade which rotates with angular velocity of 100rad…

Analysis

To solve this problem, we need to calculate the centripetal force acting on a particle moving in a circular path. We are given:

• Mass ($m$) = $10^{-2} \text{ kg}$
• Angular velocity ($\omega$) = $100 \text{ rad/s}$
• Radius ($r$) = $0.2 \text{ m}$

Concept

The centripetal force ($F_c$) is the force required to keep an object moving in a circular path. The formula relating centripetal force to angular velocity is:

Where:

• $m$ is the mass in kilograms (kg)
• $\omega$ is the angular velocity in radians per second (rad/s)
• $r$ is the radius in meters (m)

Solution

1. Identify the variables: • $m = 10^{-2} \text{ kg} = 0.01 \text{ kg}$ • $\omega = 100 \text{ rad/s}$ • $r = 0.2 \text{ m}$

2. Substitute the values into the formula: $$F_c = (0.01) \times (100)^2 \times (0.2)$$

3. Perform the calculation: • First, square the angular velocity: $100^2 = 10,000$ • Now, multiply the terms: $F_c = 0.01 \times 10,000 \times 0.2$ • $0.01 \times 10,000 = 100$ • $100 \times 0.2 = 20$

The centripetal force is 20 N.

Conclusion

Comparing our result to the given options: A. 2N B. 20N C. 200N D. 400N

The calculated value matches option B.

Exam Tip

When dealing with circular motion questions in JAMB, always check your units first! If the angular velocity were given in revolutions per minute (rpm), you would need to convert it to radians per second ($\text{rad/s}$) by multiplying by $\frac{2\pi}{60}$ before plugging it into the formula. Also, remember that $10^{-2}$ is the same as $0.01$; converting to decimals often makes the multiplication easier to handle without a calculator.