The time period of a simple pendulum is $2 \, sec$. If its length is increased $4$ times,then its period becomes ..... $\sec$.

The time period of a simple pendulum on a freely moving artificial satellite is

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

$A$ cylindrical cork of uniform density floats in a liquid of density $\rho_1$. If the cork is depressed slightly and released, it oscillates harmonically with time period $T$. If the same cork floats in another liquid of density $\rho_2$, then the similar oscillation has time period $2T$. The value of $\rho_2/\rho_1$ is :

Identify the correct statement among the following.

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