A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 m and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in m / s² ) :

Solution

Physics sir · 3 steps

The monkey rides the same circle as the man, so get ω in rad/s first and use a = ω² r.

1. Same circle. The monkey sits still on the man's shoulder, so relative to the ground it moves on the same circle of radius 9 m with the same angular speed. Its centripetal acceleration is not zero.
2. Find frequency. 120 revolutions in 3 min = 180 s gives f = 120/180 = 2/3 rev s⁻¹. So ω = 2π f = 4π/3 rad s⁻¹.

   a_c = ω² r = (4π/3)² × 9 = 16π²/9 × 9 = 16π² m s⁻²

3. So. The monkey's centripetal acceleration is 16π² m s⁻², which is option (b).

The idea to keep. Anything carried along by a body in circular motion has that body's ω. Always convert revolutions per minute into rad/s before you use a = ω² r.

Answer from the NTA final answer key. Solution by PrepWiser.