Question

A pendulum of mass $m$ hangs from a support fixed to a trolley. The direction of the string (ie angle $\theta$) when the trolley rolls up a plane of inclination $\alpha$ with acceleration $a$ is :

• A. zero
• B. ${\tan }^{-1}\alpha$
• C. ${\tan }^{-1}\frac{\alpha +g\sin \alpha }{g\cos \alpha }$
• D. ${\tan }^{-1}\frac{a}{g}$

Answer 1

The correct option is C ${\tan }^{-1}\frac{\alpha +g\sin \alpha }{g\cos \alpha }$

$\begin{array}{c}T\sin \theta =ma\alpha +mg\sin \alpha \\ T\cos \theta =mg\cos \alpha \\ \tan \theta =\left(\frac{\alpha +g\sin \alpha }{g\cos \alpha }\right)\end{array}$

Hence,

option $\left(C\right)$ is correct answer.