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 T√ρρ−1Let 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 =mg−mgρ =mg(1−mgρ) =mg(1−1ρ) =mg(ρ−1ρ) Effective acceleration geff =(ρ−1ρ)g ∴New time period T′=2π  ⎷l(ρ−1ρ)g T′=2π√lg.√ρρ−1=T√ρρ−1

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