$A$ pendulum clock is running fast. To correct its time,we should

$A$ simple pendulum of length $1 \ m$ and having a bob of mass $100 \ g$ is suspended in a car, moving on a circular track of radius $100 \ m$ with uniform speed $10 \ m/s$. If the pendulum makes small oscillations in a radial direction about its equilibrium position, then its time period is given by $T = 2\pi / \alpha^{1/4}$. The value of $\alpha$ is (Take $g = 10 \ m/s^2$)

$A$ simple pendulum having length $\ell$ has a speed of $\sqrt{2g\ell}$ at the bottom-most point of its trajectory. Its motion will be:

$A$ 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 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

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?