Two pendulums have time periods $T$ and $5T/4$. They start $SHM$ at the same time from the mean position. After how many oscillations of the smaller pendulum will they be again in the same phase?

The metallic bob of a simple pendulum has the relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water,then the new time period is given by

$A$ simple pendulum consists of a small sphere of mass $m$ suspended by a thread of length $l$. The sphere carries a positive charge $q$. The pendulum is allowed to do small oscillations in a uniform electric field $E$ with direction vertically upwards. The time period of oscillation is

$A$ simple pendulum of length $L$ is suspended from the roof of a trolley. The trolley moves in a horizontal direction with an acceleration $a$. What would be the period of oscillation of the simple pendulum? [$g$ is the acceleration due to gravity]

$A$ simple pendulum keeps correct time at $0^{\circ}C$. At $25^{\circ}C$,it loses $12.5 \, s$ in a day. What is the coefficient of linear expansion of the metal of the pendulum?

$A$ 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