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Question

The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is t0 in air. Neglecting frictional force of water and given that its density of the bob is (43)×1000 kg/m3. What relationship between t and t0 is true?

A
t=t0
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B
t=t0/2
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C
t=2t0
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D
t=4t0
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Solution

The correct option is B t=2t0
to=2πlg
Effective weight of bob inside water,
W=mgthrust=VρgVρg
Vρgeff=V(ρρ)g, where ρ= Density of bob
geff=(1ρρ)g and ρ= Density of water

t=2πlgeff=2πl(1ρ/ρ)g

tt0=1(1ρ/ρ)=  1134 (ρ=103 kg/m3 ρ=43×103kg/m3)
t=2t0.

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