Question

The period of oscillation of a simple pendulum of length l suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$, is given by

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Since the vehicle is moving down the plane with an acceleration
$g\sin \alpha$ & and the bob moves with same acceleration (because, each and every particle of the system is accelerating with same acceleration down the plane) the string will remain perpendicular to the plane.

$\Rightarrow$ When the bob is released, it moves down perpendicular to the base of the vehicle relative to vehicle with an acceleration
$g^{{}^{\prime }}=\sqrt{g^2-g^2{\sin }^2\alpha }=g\cos \alpha$
$\Rightarrow$ The period of oscillation of the pendulum
$=2\pi \sqrt{\frac{l}{g^{{}^{\prime }}}}=2\pi \sqrt{\frac{l}{g\cos \alpha }}$
The pendulum will oscillate about the mean position that is given by the perpendicular position of the thread to the base of the vehicle.