First slide

Applications of SHM

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 = $(mg - \frac{m}{ρ} g) = mg (\frac{ρ - 1}{ρ})$ $∴ g_{eff} = g (\frac{ρ - 1}{ρ})$
$\frac{T'}{T} = \sqrt{\frac{g}{g_{e f f}}} T_{1} \Rightarrow T^{'} = T \sqrt{\frac{ρ}{(ρ - 1)}}$

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