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>> $The time period of a simple pendulum is$

Question

The time period of a simple pendulum is air is $T$ . Now the pendulum is submerged in a liquid of density $\frac{ρ}{1 6}$ where $ρ$ is density of the bob of the pendulum. The new time period of oscillation is.

A

$\frac{4}{1 5} T$

B

$\frac{4}{1 5} T$

C

$\frac{1 5}{4} T$

D

$\frac{1 5}{4} T$

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Updated on : 2022-09-05

Solution

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Correct option is A)

$T = 2 π \frac{ℓ}{g}$
$τ = I α$
$(ρ V g - \frac{ρ}{1 6} V g) ℓ sin θ = (ρ V) ℓ^{2} α$
$\frac{1 5 g}{1 6 ℓ} θ = α$
$ω = \frac{1 5 g}{1 6 ℓ} \Rightarrow T^{'} = 2 π \frac{1 6 ℓ}{1 5 g}$
$T^{'} = \frac{4}{1 5} T$

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