Question

A simple pendulum is oscillating in a trolley moving on a horizontal straight road with constant acceleration a. If direction of motion of trolley is taken as positive $x$ direction and vertical upward direction as positive $y$ direction then the mean position of pendulum makes an angle

• A. ${\tan }^{-1}\left(\frac{g}{a}\right)$ with $y$ axis in $+x$ direction
• B. ${\tan }^{-1}\left(\frac{a}{g}\right)$ with $y$ axis in $-x$ direction
• C. ${\tan }^{-1}\left(\frac{a}{g}\right)$ with $y$ axis in $+x$ direction
• D. ${\tan }^{-1}\left(\frac{g}{a}\right)$ with $y$ axis in $-x$ direction

Answer 1

Answer: (B)

$T\sin \theta =ma$ ... (i)
$T\cos \theta =mg$ ... (ii)
Dividing (i) and (ii)
$T\cos \theta -\frac{a}{g}$
$\theta ={\tan }^{-1}\left(\frac{a}{g}\right)$