First slide

Applications of SHM

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 $t_{0}$ in air. Neglecting frictional force of water and given that the density of the bob is (4/3) ×1000 kg/m3. What relationship between $t$ and $t_{0}$ is true [AIEEE 2004]

Moderate

A

$t = t_{0}$
B

$t = t_{0} / 2$
C

$t = 2 t_{0}$
D

$t = 4 t_{0}$

Solution

$∵ t_{o} = 2 π \sqrt{\frac{l}{g}}$
Effective weight of bob inside water,
$W^{'} = mg - thrust = Vρg - {Vρ}^{'} g$
$\Rightarrow {Vρg}_{eff} = V (ρ - ρ^{'}) g,$ where, $ρ$ = Density of bob
$\Rightarrow g_{eff} = (1 - \frac{ρ^{'}}{ρ}) g$ and $ρ^{'}$ = Density of water
$∴ t = 2 π \sqrt{\frac{l}{g_{eff}}} = 2 π \sqrt{\frac{l}{(1 - ρ^{'} / ρ) g}}$
$∴ \frac{t}{t_{0}} = \sqrt{\frac{1}{1 - ρ^{'} / ρ}} = \sqrt{\frac{1}{1 - \frac{3}{4}}}$ =2 $\begin{array}{l} (∵ ρ^{'} = 10^{3} kg / m^{3} \\ ρ = \frac{4}{3} \times 10^{3} kg / m^{3} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App