Two simple pendulums $A$ and $B$ are made to oscillate simultaneously. It is found that $A$ completes $10$ oscillations in $20 \ s$ and $B$ completes $8$ oscillations in $10 \ s$. The ratio of the lengths of $A$ and $B$ is

$A$ 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).

The breaking strength of the string of a simple pendulum is twice the weight of the bob. The bob is released from rest when the string is horizontal. At what angle $\theta$ with the vertical will the string break?

Define a simple pendulum and the length of the pendulum.

The length of a second's pendulum on the surface of the earth is $1 \ m$. What will be the length of a second's pendulum on the moon?

$A$ pendulum clock is placed inside an elevator. Under what condition does it show the correct time?