A ring is formed by joining two uniform semi circular rings ABC a… - Vidyadip

MCQ

A ring is formed by joining two uniform semi circular rings $ABC$ and $ADC$. Mass of $ABC$ is thrice of that of $ADC$. If the ring is hinged to a fixed support ,at $A$, it can rotate freely in a vertical plane. Find the value of $tan\,\theta$, where $\theta$ is the angle made. by the line $AC$ with the vertical in equilibrium

A
$\frac{{9\pi }}{4}$
✓
$\frac{{1 }}{\pi}$
C
$\frac{{2 }}{3\pi}$
D
$\pi$

✓

Answer

Correct option: B.

$\frac{{1 }}{\pi}$

b
$\mathrm{X}_{\mathrm{com}}=\frac{-\mathrm{R}}{\pi}$

$\tan \theta=\frac{\mathrm{R}}{\pi \mathrm{R}}=\frac{1}{\pi}$

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