Question

A plumb bob is hung from the ceiling of a train compartment. The train moves on an inclined track of inclination ${30}^{\circ }$ with horizontal. Acceleration of train up the plane is $a=\frac{g}{2}$. The angle which the string supporting the bob makes with normal to the ceiling in equilibrium is $\theta$. Then $\tan \theta$ upto 2 decimal places is

Answer 1

$T\sin \theta -mg\sin {30}^{\circ }=ma$
$\Rightarrow T\sin \theta =mg\sin {30}^{\circ }+\frac{mg}{2}$
$T\cos \theta =mg\cos {30}^{\circ }$
Dividing equation (i) by (ii), we get

$\tan \theta =\frac{2}{\sqrt{3}}$