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 the density of the bob is (4/3) ×1000 kg/m3. What relationship between t and t0 is true [AIEEE 2004]
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a
t=t0
b
t=t0/2
c
t=2t0
d
t=4t0
answer is C.
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Detailed Solution
∵ to=2 πlgEffective weight of bob inside water,W'=mg−thrust=Vρg−Vρ'g⇒Vρgeff=V(ρ−ρ')g, where, ρ= Density of bob ⇒geff=1−ρ'ρ g and ρ'= Density of water∴t=2 πlgeff=2 πl(1−ρ'/ρ)g∴tt0=11−ρ'/ρ=11−34 =2 (∵ρ'=103kg/m3 ρ=43×103kg/m3