A lady wears an ear-ring suspended by a light wire of length 3 cm . She sits in a merry-go-round that moves at 4 m/s in a circle of radius 2 m . Determine the time period of small oscillations of the ear-ring.

Step-by-step solution

The lady is in a rotating frame of reference, so the ear-ring experiences a centrifugal acceleration in addition to gravity. Centripetal acceleration of the merry-go-round is given by: a = v^2 R = 4^2 2 = 8 m/s ^2 The effective acceleration due to gravity g_ eff is the vector sum of the acceleration due to gravity g and the horizontal acceleration a : g_ eff = g^2 + a^2 Taking g = 10 m/s ^2 : g_ eff = 10^2 + 8^2 = 164 12.8 m/s ^2 The time period of small oscillations for a simple pendulum is: T = 2 l g_ eff Given l