At a given place, to increase the number of oscillations made by a simple pendulum in one minute from $72$ to $90$, the length of the pendulum is to be decreased by (in $\%$)

$A$ simple pendulum of length $L$ is suspended from the roof of a trolley. The trolley moves in a horizontal direction with an acceleration $a$. What would be the period of oscillation of the simple pendulum? [$g$ is the acceleration due to gravity]

$A$ pendulum clock that keeps correct time on the earth is taken to the moon. It will run (given that $g_{Moon} = g_{Earth}/6$):

The motion of a simple pendulum executing $S.H.M.$ is represented by the following equation:
$Y = A \sin (\pi t + \phi)$,where time is measured in $seconds$.
The length of the pendulum is .............$cm$.

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 $\alpha$,is given by

$A$ chimpanzee swinging on a swing in a sitting position,stands up suddenly,the time period will