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

The periodic time of a simple pendulum of length $1\, m$ and amplitude $2\, cm$ is $5\, s$. If the amplitude is made $4\, cm$,its periodic time in seconds will be

The time period of a simple pendulum in air is $T$. If the pendulum is immersed in water and executes $SHM$,its time period is $t$. The value of $\frac{T}{t}$ is [density of the bob is $\frac{5000}{3} \ kg \ m^{-3}$ and density of water is $1000 \ kg \ m^{-3}$].

The bob of a simple pendulum having length $l$ is displaced from the mean position to an angular position $\theta$ with respect to the vertical. If it is released,then the velocity of the bob at the equilibrium position is:

$A$ simple pendulum of time period $1\,s$ and length $l$ is hung from a fixed support at $O$. The bob is at a distance $H$ vertically above $A$ on the ground. The amplitude is $\theta_0$. The string snaps at $\theta = \frac{\theta_0}{2}$. Find the time taken by the bob to hit the ground and the distance from $A$ where the bob hits the ground. Assume $\theta_0$ to be small,so that $\sin \theta_0 \approx \theta_0$ and $\cos \theta_0 \approx 1$.