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Question

A simple pendulum with a solid metal bob has a period T. The metal bob is now immersed in a liquid of density one tenth that of the bob. The liquid is non-viscous. Now the period of the same pendulum with its bob remaining all the time in the liquid will be

A
T
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B
9T10
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C
109 T
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D
910 T
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Solution

The correct option is C 109 T
Let us represent the combined gravitational force and buoyant force acting on the mass as mg.

Let ρs be the density of solid bob and ρl be the density of liquid.

Now, mg=mgρlVg

ρsVg=ρsVgρlVg

g=g[1ρlρs]

g=g(1ρlρs)

As, ρl=ρs10

g=g(1110)=910g

As, T1geffective

TT=gg

T=109 T

Hence, option (C) is correct.

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