$A$ pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is $20 \; m/s^2$ at a distance of $5 \; m$ from the mean position. The time period of oscillation is

$A$ simple pendulum of length $L$ has mass $m$ and it oscillates freely with amplitude $A$. At the extreme position,its potential energy is ($g =$ acceleration due to gravity).

$A$ hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom,the period of oscillation will

$A$ seconds pendulum is placed in a space laboratory orbiting round the Earth at a height $3R$ from the Earth's surface. The time period of the pendulum will be ($R =$ radius of Earth).

For a simple pendulum, the graph of time period $(T)$ versus length $(l)$ is depicted by:

$A$ 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 $\cos \theta_0 \approx 1$.