13.Oscillations
medium

A simple pendulum with a metallic bob has a time period $T$. The bob is now immersed in a non-viscous liquid and oscillated. If the density of the liquid is $1 / 4$ that of metal, the time period of the same pendulum will be ...........

A

$\frac{T}{\sqrt{3}}$

B

$\frac{2 T}{\sqrt{3}}$

C

$\frac{4}{3} T$

D

$\frac{2}{3} T$

Solution

(b)

Normal time period $T=2 \pi \sqrt{\frac{l}{g}}$

When immersed in a liquid. It experiences an upthrust.

Upthrust $=\frac{\rho}{4} \times$ volume $g$

Upward acceleration $=$ Upward force $/$ mass of ball $=\frac{g}{4}$

$T^{\prime}=2 \pi \sqrt{\frac{I}{g_{e f f}}}$

$g_{\text {eff }}=g-\frac{g}{4}=\frac{3}{4} g$

$T^{\prime}=2 \pi=\sqrt{\frac{1}{3 g} \times 4}=\frac{2 T}{\sqrt{3}}$

Standard 11
Physics

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