$A$ simple pendulum of length $L$ swings in a vertical plane. The tension in the string when it makes an angle $\theta$ with the vertical and the bob of mass $m$ moves with a speed $v$ is (where $g$ is the gravitational acceleration):

$A$ cylindrical piece of cork of density $\rho$, base area $A$, and height $h$ floats in a liquid of density $\rho_{l}$. The cork is depressed slightly and then released. Show that the cork oscillates up and down simple harmonically with a period $T=2 \pi \sqrt{\frac{h \rho}{\rho_{l} g}}$. (Ignore damping due to viscosity of the liquid).

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

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 .............$cm$.

$A$ pendulum is swinging in an elevator. Its period will be greatest when the elevator is

$A$ string of a pendulum of length $l$ is displaced through $90^{\circ}$ from its vertical and released. Then,the minimum strength of the string needed to withstand the tension as the pendulum passes through its mean position is