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)

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