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Question

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

A
T(ρ1ρ)
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B
T(ρρ1)
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C
Tρ1ρ
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D
Tρρ1
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Solution

The correct option is D Tρρ1
Let the mass of the bob be m, then its volume
=mρb
Upthrust on bob when immersed in water =mρb×ρw×g=mgρ
Apparent weight of the bob
=mgmgρ
=mg(1mgρ)
=mg(11ρ)
=mg(ρ1ρ)
Effective acceleration geff
=(ρ1ρ)g
New time period T=2π  l(ρ1ρ)g
T=2πlg.ρρ1=Tρρ1

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