A simple pendulum of length `l` is suspended from the celing of a cart which is sliding without friction on as inclined plane of inclination theta . What will be the time period of the pendulum?

Explanation

When the cart is at rest, the effective acceleration due to gravity is g and when the cart is rolling down the inclined surface, the effective acceleration due to gravity involved perpendicular to plane is gco`theta`. Tiem period of pendulum when cart is immobile,
`T=2pisqrt((l)/(g))`
Time period of pendulum when cart is moving down the plane,
`T^(')=2pisqrt((l)/(gcostheta))=(T)/sqrt(costheta)`