Question

A simple pendulum has a time period T. The pendulum is completely immersed in a non-viscous liquid, whose density is 1/10th of that of the material of the bob. The time period of the pendulum is immersed in the liquid is?

(a) T

(b) T/10

(c) √(9/10) T

(d) √(10/9) T

This question was addressed to me in an international level competition.

Enquiry is from Oscillatory Motion topic in portion Oscillations of Engineering Physics I

Answer 1

The correct choice is (d) √(10/9) T

To elaborate: In air, T=2π√(l/g)

Let ρ be the density of the bob material. When the bob is immersed in a non-viscous liquid of density ρ0=ρ/10, time period becomes

T=2π√(l/(1-(ρ0/ρ))g)=2π√(l/(9/10)g)

T=√(10/9) T.