If $R$ is the radius of the earth and the acceleration due to gravity on the surface of the earth is $g = \pi^2 \ m/s^2$,then the length of the second's pendulum at a height $h = 2R$ from the surface of the earth will be:

At what position is the speed of a simple pendulum maximum?

Two simple pendulums have first $(A)$ bob of mass $M_1$ and length $L_1$,second $(B)$ of mass $M_2$ and length $L_2$. Given $M_1 = M_2$ and $L_1 = 2 L_2$. If their total energies are the same,then which of the following statements is correct?

If a body dropped freely from a height of $20 \,m$ reaches the surface of a planet with a velocity of $31.4 \,ms^{-1}$, then the length of a simple pendulum that ticks seconds on the planet is (in $\,m$)

Two masses,both equal to $100\, g$,are suspended at the ends of identical light strings of length $\ell = 1.0\, m$,attached to the same point on the ceiling (see figure). At time $t = 0$,they are simultaneously released from rest,one at angle $\theta_1 = 1^o$,the other at angle $\theta_2 = 2^o$ from the vertical. The masses will collide

Two simple pendulums of lengths $1.44 \, m$ and $1 \, m$ start swinging together. After how many vibrations will they again start swinging together?