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 ?
It is given that the length of a simple pendulum is l , the mass of bob is M , the radius of a circular track is R and the uniform speed is ν .
The formula of centripetal acceleration is,
a c = ν 2 R
The effective acceleration due to gravity is,
g 1 = g 2 + a c 2
Substitute the values.
g 1 = g 2 + ν 4 R 2
The formula of time period is,
T 1 = 2 π l g 1
Substitute the values.
T 1 = 2 π l g 2 + ν 4 R 2
Hence, the time period, T 1 = 2 π l g 2 + ν 4 R 2
It is given that the length of a simple pendulum is
The formula of centripetal acceleration is,
The effective acceleration due to gravity is,
Substitute the values.
The formula of time period is,
Substitute the values.
Hence, the time period,
