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The time 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 : (1) 2π√(L/(g cosα)) (2) 2π√(L/(g sinα)) (3) 2π√(L/g) (4) 2π√(L/(g tanα))

1. 2π√(L/(g cosα))
2. 2π√(L/(g sinα))
3. 2π√(L/g)
4. 2π√(L/(g tanα))

Correct answer: 2π√(L/(g sinα))

Solution

The correct option is based on the effective gravitational force acting on the pendulum when the vehicle is on an incline. The component of gravitational acceleration acting along the direction of the pendulum's motion is reduced by the sine of the angle of inclination, which modifies the period of oscillation accordingly.

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