Question

A pendulum bob of mass m is attached to the ceiling of a cart which is accelerating with $a_0$ as shown below. Find the angle made by the bob with the vertical.

Answer 1

$Tsin\theta =m{a}_0$ ...... (1)
and $Tcos\theta =mg$ ...... (2)
From equations (1) and (2),
$\frac{sin\theta }{cos\theta }=\frac{m{a}_0}{mg}$
$\Rightarrow tan\theta =\frac{a_0}{g}$
$\therefore \theta =ta{n}^{-1}\frac{a_0}{g}$