NEET Physics Question - Laws of Motion

A truck is stationary and has a bob suspended by a light string, in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of a. The pendulum will tilt

To the left and angle of inclination of the pendulum with the vertical is tan-¹(g/a)

To the left and angle of inclination of the pendulum with the vertical is sin-¹(g/a)

To the left and angle of inclination of the pendulum with the vertical is tan-¹(a/g)

To the left and angle of inclination of the pendulum with the vertical is sin-¹(a/g)

Solution:

When the truck accelerates to the right with $a$ , a pseudo force $ma$ acts to the left on the bob in the truck's frame. The bob reaches equilibrium where the tension components balance forces:

$\tan \theta = \frac{\text{Pseudo force}}{\text{Weight}} = \frac{ma}{mg} = \frac{a}{g}$ $\theta = \tan^{-1} \left(\frac{a}{g} \right)$

Thus, the pendulum tilts to the left at an angle $\theta = \tan^{-1}(a/g)$ with the vertical.

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