Question

A body is pivoted so that its center of gravity is 2.5m from the axis of rotation. The body's radius of gyration is 20cm. The body acts like a physical pendulum. What is the period of vibration of the body? a. 0.01s b. 0.1s c. 0.11s d. 1.0s

Answer 1

The period of vibration of the body is 0.11s.

Step-by-step explanation:

In order to find the period of vibration of a body acting like a physical pendulum, we need to use the formula:

T =
`2* pi * √((I/mgh))`

Where:

T is the period of vibration,

I is the moment of inertia of the body about the axis of rotation,

m is the mass of the body,

g is the acceleration due to gravity, and

h is the distance between the center of gravity and the axis of rotation.

In this case, the radius of gyration is given, which is equal to the moment of inertia divided by the mass. So we can rewrite the formula as:

T = 2π
`√(kgh)`

Substituting the given values, we have:

T = 2π
`√((0.2^2)(9.8)(2.5)))` = 0.11 s