Question

A pendulum of mass m hangs from a support fixed to a trolley. The direction of the string when the trolley rolls up a plane of inclination $\alpha$ with acceleration $a_0$ is

• A. $\theta =\tan {}^{-1}\alpha$
• B. $\theta =\tan {}^{-1}\left(\frac{a_0}{g}\right)$
• C. $\theta =\tan {}^{-1}\left(\frac{g}{a_0}\right)$
• D. $\theta =\tan {}^{-1}\left(\frac{a_0+g\sin \alpha }{g\cos \alpha }\right)$

Answer 1

The correct option is D $\theta =\tan {}^{-1}\left(\frac{a_0+g\sin \alpha }{g\cos \alpha }\right)$

$\begin{array}{c}T\sin \theta =m{a}_0+mg\sin a\\ T\cos \theta =mg\cos a\\ \tan \theta =\left(\frac{a_0+g\sin \alpha }{g\cos \alpha }\right)\end{array}$

Hence,

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