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Question: The metallic bob of simple pendulum has the relative density *ρ*. The time period of this pendulum i...

The metallic bob of simple pendulum has the relative density ρ. The time period of this pendulum is T. If the metallic bob is immersed in water, then the new time period is given by

A

T(ρ−1ρ)T\left( \frac{\rho - 1}{\rho} \right)

B

T(ρρ−1)T\left( \frac{\rho}{\rho - 1} \right)

C

Tρ−1ρT\sqrt{\frac{\rho - 1}{\rho}}

D

Tρρ−1T\sqrt{\frac{\rho}{\rho - 1}}

Answer

Tρρ−1T\sqrt{\frac{\rho}{\rho - 1}}

Explanation

Solution

Formula T′T=ρρ−σ\frac{T'}{T} = \sqrt{\frac{\rho}{\rho - \sigma}} Here σ=1\sigma = 1for water

so T′=Tρρ−1T' = T\sqrt{\frac{\rho}{\rho - 1}}.