Question

A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period?

Answer 1

The bob of the simple pendulum will experience the acceleration due to gravity and the centripetal acceleration provided by the circular motion of the car.

Acceleration due to gravity = g

Centripetal acceleration

Where,

v is the uniform speed of the car

R is the radius of the track

Effective acceleration (a_eff) is given as:

Time period,

Where, l is the length of the pendulum

∴Time period, T