A disc of radius r and mass m is pivoted at its rim an asset to small oscillation of a simple pendulum has time period then effective length of pendulum is
Answers
Effective length of pendulum is,
Explanation:
Moment of inertia of the disc about the axis of oscillation is,
Time period of the pendulum,
..............(1)
Consider a simple pendulum having effective length l has the same time period,
.................(2)
Equating eq. 1 and 2
Thus, is the length of pendulum.
Given that,
Radius of disc= r
Mass = m
We need to calculate the moment of inertia at rim
Using parallel theorem
Put the value into the formula
We need to calculate the time period
Using formula of time period
Here, d = distance between point of suspension and center of gravity
Put the value into the formula
......(I)
We need to calculate the effective length of the pendulum
Using formula of time period
On compare of time period from equation
The effective length is
Hence, The effective length of the pendulum is .