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 the air. Neglecting frictional force of water and given that the density of the bob is (4/3) x 1000 ms-1 . What relationship between t and t0 is true?
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t = t0
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t = t0/2
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t = 2t0
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t = 4t0
Solution
C.
t = 2t0
The time period of simple pendulum in air
being the length of simple pendulum, In water, effective weight of bob
w' = weight of bob in air - upthrust
⇒ ρVgeff = mg-m'g = ρVg-ρ'Vg = (ρ-ρ') where ρ = density of bob, ρ′ = density of water
