Consider a simple pendulum is hanging in a accelerated railroad car. Pendulum makes an angle $\theta$ with the vertical. Find value of $\theta$ (In inertial frame).

In inertial frame: To an observer on the ground, the forces on the bob of pendulum are;

I. Weight of $mg$ acts vertically downward.

II. Tension in the string $T$ .

Thus for the motion of bob relative to an observer on the ground,

                                 $T \sin \theta = ma$ ,                …(i)

and                           $T \cos \theta = mg$ .               …(ii)

Dividing equation (i) by (ii), we get

$\tan \theta = \frac{a}{g}$ .