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

$A$ cylindrical block of wood (density $= 650 \ kg \ m^{-3}$),of base area $30 \ cm^2$ and height $54 \ cm$,floats in a liquid of density $900 \ kg \ m^{-3}$. The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length ..... $cm$ (nearly).

$A$ tunnel has been dug through the centre of the Earth and a ball is released in it. It will reach the other end of the tunnel after:

The length of a simple pendulum is increased by $1\%$. Its time period will

The ratio of frequencies of two pendulums is $2 : 3$. What is the ratio of their lengths?

$A$ simple pendulum is made of a body which is a hollow sphere containing mercury, suspended by means of a wire. If a little mercury is drained off, the period of the pendulum will