Question

A pendulum hanging from the ceiling of a railway carriage make an angle of ${30}^{\circ }$ with the vertical when it is accelerating. Find the acceleration of the carriage.

• A. $\frac{\sqrt{3}g}{2}$
• B. $\frac{2g}{\sqrt{3}}$
• C. $g\sqrt{3}$
• D. $\frac{g}{\sqrt{3}}$

Answer 1

The correct option is D $\frac{g}{\sqrt{3}}$

The given system can be shown in the carriage frame as

From the carriage's frame, pseudoforce $F=ma$ will be acting on the bob in the opposite direction of acceleration.


So, from the FBD of the bob we get
$T\cos \theta =mg$ and $T\sin \theta =ma$

From these two equations we get,
$a=g\tan \theta =g\tan {30}^{\circ }=\frac{g}{\sqrt{3}}$