If a body dropped freely from a height of $20 \,m$ reaches the surface of a planet with a velocity of $31.4 \,ms^{-1}$, then the length of a simple pendulum that ticks seconds on the planet is (in $\,m$)

$A$ pendulum suspended from the ceiling of a train has a period $T$,when the train is at rest. When the train is accelerating with a uniform acceleration $a$,the period of oscillation will

Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $\theta_1$ and $\theta_2$ from their mean positions,respectively. If the angular accelerations of both pendulums are same,then which expression is correct?

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

$A$ ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle $(\theta)$ of thread deflection in the extreme position will be :

$A$ simple pendulum,suspended from the ceiling of a stationary van,has time period $T$. If the van starts moving with a uniform velocity,the period of the pendulum will be