$A$ simple pendulum executing $S.H.M.$ is falling freely along with its support. Then:

$A$ simple pendulum,suspended from the ceiling of a stationary van,has time period $T$. If the van starts moving with a uniform velocity,the period of the pendulum will be

Choose the correct length $(L)$ versus square of time period $(T^2)$ graph for a simple pendulum executing simple harmonic motion.

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:

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?

Two pendulums of length $1.21 \,m$ and $1.0 \,m$ start vibrating. At some instant,the two are in the mean position in the same phase. After how many vibrations of the longer pendulum will the two be in phase again?