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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 θ, is given by

a
2πLgcosθ
b
2πLgsinθ
c
2πLg
d
2πLgtanθ

detailed solution

Correct option is A

See the following force diagram.Vehicle is moving down the frictionless inclined surface so, it's acceleration is gsinθ . Since vehicle is accelerating, a pseudo force  m(gsinθ) will act on bob of pendulum which cancel the sinθ component of weight of the bob.Hence net force on the bob is Fnet =mgcosθ or net acceleration of the bob is  geff=gcosθ∴ Time period  T=2πLgeff=2πLgcosθ

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