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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 α, is given by

A
2πLgcosα
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B
2πLgsinα
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C
2πLg
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D
2πLgtanα
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Solution

The correct option is A 2πLgcosα
Since the vehicle is moving down the plane with an acceleration
gsinα and the bob moves with same acceleration (because, each and every particle of the system is accelerating with same acceleration down the plane).
When the bob is released, it moves with effective acceleration of
geff=g2g2sin2α=gcosα
The period of oscillation of the pendulum
=2πlg=2πlgcosα

OR

As pendulum is in non-inertial frame,
Applying psuedo force Fp=mgsinα, along the plane,
On diving mg into components, we get mgsinα along the plane and mgcosα perpendicular to plane.
Hence along the plane Fp and mgsinα balance each other and mgcosα causes oscillation
Effective acceleration is a=gcosα
The period of oscillation of the pendulum
=2πlg=2πlgcosα

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