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 a, is given by

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

See the following force diagram

Vehicle is moving down the frictionless inclined surface so, it's acceleration is g sin $\theta$. Since vehicle is accelerating, a pseudo force m(g sin $\theta )$ will act on bob of pendulum which cancel the $sin\theta$ component of weight of the bob.
Hence net force on the bob is $F_{net}=mgcos\theta$ or net acceleration of the bob is $g_{eff}=gcos\theta$

$\therefore$ Time period $T=2\pi \sqrt{\frac{1}{g_{eff}}}=2\pi \sqrt{\frac{1}{gcos\theta }}$