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 α, is given by
2π√lgcosα
2π√1gsinα
2π√lg
2π√lgtanα
A
2π√lgcosα
B
2π√lg
C
2π√1gsinα
D
2π√lgtanα
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Solution
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We are given that the simple pendulum of length l is hanging from the roof of a vehicle which is moving down the frictionless inclined plane. So, its 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 we can say that the effective acceleration would be equal to geff=gcosα Now the time period of oscillation is given by T=2π√1geff=2π√lgcosα l
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