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Q.

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 (43) × 1000 kg/m3. Which relationship between t and t0 is true?

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a

t = t0

b

t = t02

c

t = 2t0

d

t = 4t0

answer is C.

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Detailed Solution

∴ t0 = 2πlgEffective weight of bob inside water,W' = mg - thrrust = Vρg-Vρ`g⇒Vρgeff= V(ρ-ρ1)g, where, ρ = Density of bob⇒geff = (1-ρ'ρ)g and ρ' = Density of water∴ t = 2πlgeff = 2πl(1-ρ'ρ)g∴  tt0 = 11-ρ'ρ = 11-34(∵  ρ' = 103kg/m3 and ρ = 43×103kg/m3) ⇒t = 2 t0
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