In an experiment for determining the gravitational acceleration $g$ of a place with the help of a simple pendulum,the measured time period square $(T^2)$ is plotted against the string length $(L)$ of the pendulum as shown in the figure. What is the value of $g$ at the place in $m/s^2$?

$A$ $50 \ cm$ long simple pendulum is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration $\sqrt{3} \ g \ m/s^2$. The time period of small oscillations of the pendulum about its equilibrium position is $.... \ s$ $\left(g=\pi^2 \ m/s^2\right):-$

If the time period of a $2 \ m$ long simple pendulum is $2 \ s$,the acceleration due to gravity at the place where the pendulum is executing $S.H.M.$ is

$A$ pendulum oscillates simple harmonically if and only if:
$I$. The size of the bob of the pendulum is negligible in comparison with the length of the pendulum.
$II$. The angular amplitude is less than $10^{\circ}$.
Choose the correct option.

$A$ 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).

$A$ simple pendulum of length $L$ has mass $M$ and it oscillates freely with amplitude $A$. At the extreme position,its potential energy is: