Question

If the mass moment inertia of the object is increased to 4 times then what will be the effect of time period of the compound pendulum?

(a) Doubled

(b) Remains same

(c) Halved

(d) Decreases by √2 times

The question was posed to me during an internship interview.

My enquiry is from Compound Pendulum in division Simple Harmonic Motion of Machine Kinematics

Answer 1

Correct option is (a) Doubled

To explain I would say: The time period of a compound pendulum is given by:

(2π)\(\sqrt{(\frac{I}{mgl})}\), now the dependency of the time period on the mass moment of inertia is directly proportional to the root of Moment of Inertia, hence it increases by 2 times.