From the ceiling of a train, a pendulum of length 'l' is suspended. The train is moving with an acceleration `a_(0)` on horizontal surface. What must be the period of oscillation of pendulum?

Explanation

Acceleration a of the plane can be resolved in two rectangular components
`a_(x) = a cos theta`
`a_(y) = a sin theta`
The flying aeroplane can be considered as a lift moving upwards with a vertical acceleration `a_(y)`, So, the effective downward acceleration is `a. = g + a sin theta`.
The time period of oscillation of simple pendulum thus becomes
`T = 2pisqrt((l)/(g + a cos theta))`
If we consider horizontal components of acceleration. Also, then effective acceleration due to gravity is further increased. Hence time period decreases.