First slide

Simple harmonic motion

Question

The metallic bob of a simple pendulum has the relative density $ρ$ . The time period of this pendulum is T. If the metallic bob is immersed in water, then the new time period is given by

Moderate

A

$T \frac{ρ - 1}{ρ}$
B

$T \frac{ρ}{ρ - 1}$
C

$T \sqrt{\frac{ρ - 1}{ρ}}$
D

$T \sqrt{\frac{ρ}{ρ - 1}}$

Solution

When the bob is immersed in water, its effective weight $= (m g - \frac{m}{ρ} g) = m g (\frac{ρ - 1}{ρ}) ∴ g_{e f f} = g (\frac{ρ - 1}{ρ})$
$\frac{T^{'}}{T} = \sqrt{\frac{g}{g_{e f f}}}$

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