The time period of a simple pendulum of length $L$ as measured in an elevator descending with acceleration $\frac{g}{3}$ is

The bob of a simple pendulum of mass $m$ and total energy $E$ will have maximum linear momentum equal to

$A$ pendulum oscillates simple harmonically if and only if:
$I$. The size of the bob of the pendulum is negligible in comparison with the length of the pendulum.
$II$. The angular amplitude is less than $10^{\circ}$.
Choose the correct option.

$A$ 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 :

What is the frequency of oscillation of a pendulum suspended in a freely falling lift?

$A$ simple pendulum is suspended in a lift which is going up with an acceleration $5 \ m/s^2$. An electric field of magnitude $5 \ N/C$ and directed vertically upward is also present in the lift. The charge of the bob is $1 \ mC$ and mass is $1 \ mg$. Taking $g = \pi^2 \ m/s^2$ and length of the simple pendulum $1 \ m$,the time period of the simple pendulum is ...... $s$.