Question

A bob of mass $m=50\text{kg}$ is suspended from the ceiling of a trolley by a light inextensible string. If the trolley accelerates horizontally, the string makes an angle ${30}^o$ with the vertical. Find the acceleration of the trolley.

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

Answer 1

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

From frame of trolley
$T\sin \theta =ma$
$T\cos \theta =mg$
$\frac{a}{g}=\frac{\sin \theta }{\cos \theta }$
$a=g\tan \theta$ $(\theta ={30}^o)$
$=g/\sqrt{3}$