Question

A bob of mass $m$ is suspended from a ceiling of a trolley by a light inextensible string. When the trolley accelerates horizontally, the string makes an angle $\theta$ with the vertical. Then choose the correct statement.

• A. $\theta$ depends on the acceleration of trolley only
• B. $\theta$ depends on the acceleration of trolley and acceleration due to gravity
• C. $\theta$ depends on mass of bob, acceleration of trolley and acceleration due to gravity.
• D. none of these

Answer 1

The correct option is B $\theta$ depends on the acceleration of trolley and acceleration due to gravity

If an observer is sitting in the trolley observes the bob, he will observe the bob to be at rest. If we draw $FBD$ in his frame of reference, a pseudo force $\left(ma\right)$ will seem to act on the bob towards the left.


Therefore, in vertical direction,
$T\cos \theta =mg-\left(i\right)$
and in horizontal direction
$T\sin \theta =ma-\left(ii\right)$

Hence, from $\left(i\right)$ and $\left(ii\right)$
$\tan \theta =\frac{a}{g}\Rightarrow \theta ={\tan }^{-1}\frac{a}{g}$
Therefore, $\theta$ depends on the acceleration of trolley and acceleration due to gravity only.