A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4 \mathrm{~m}$, then the time period of small oscillations will be ____ $s$. $\left[\right.$ take $\left.\mathrm{g}=\pi^2 \mathrm{~ms}^{-2}\right]$

The period of oscillation of a simple pendulum of constant length at earth surface is $T$. Its period inside a mine is

A simple pendulum consisting of a ball of mass $m$ tied to a thread of length $l$ is made to swing on a circular arc of angle $\theta $ in a vertical plane. At the end of this arc, another ball of mass $m$ is placed at rest. The momentum transferred to this ball at rest by the swinging ball is

A pendulum clock that keeps correct time on the earth is taken to the moon it will run (it is given that $g_{Moon} = g_{Earth}/6$ )

The length of a second's pendulum on the surface of earth is $1\, m$. What will be the length of a second's pendulum on the moon ?