The length of a seconds pendulum at a height $h=2 R$ from earth surface will be.(Given: $R =$ Radius of earth and acceleration due to gravity at the surface of earth $g =\pi^{2}\,m / s ^{-2}$ )

If the length of a clock pendulum increases by $0.2 \%$ due to atmospheric temperature rise, then the loss in time of clock per day is ........... $s$

Given below are two statements:

Statement $I :$ A second's pendulum has a time period of $1$ second.

Statement $II :$ It takes precisely one second to move between the two extreme positions.

In the light of the above statements, choose the correct answer from the options given below:

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

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

A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than $90^o$. At its highest point, the string is cut. Which trajectory is possible for the bob afterwards.