The ratio of frequencies of two oscillating pendulums are $3: 2$. Their lengths are in the ratio:

$A$ simple pendulum of length ' $\ell$ ' has a bob of mass 'm'. It executes $S$.$H$.$M$. of small amplitude '$A$'. The maximum tension in the string is ($g=$ acceleration due to gravity).

The bob of a simple pendulum is hanging vertically down from a fixed identical bob by means of a string of length $l$. If both bobs are charged with a charge $q$ each, what is the time period of the pendulum? (Ignore the radii of the bobs.)

What happens to the time period of a simple pendulum when it is taken to the moon's surface from the earth's surface?

What is the velocity of the bob of a simple pendulum at its mean position,if it is able to rise to a vertical height of $10\,cm$ $(g = 9.8\,m/s^2)$?

$A$ small sphere of radius $r$ is placed on a concave surface of radius of curvature $R$ a little away from the center. When the sphere is released, it oscillates. Assuming the oscillation to be simple harmonic motion and $r << R$, then the time period is