$A$ man measures the period of a simple pendulum inside a stationary lift and finds it to be $T$ seconds. If the lift accelerates upwards with an acceleration of $\frac{g}{4}$,then the period of the pendulum will be

$A$ light balloon filled with helium of density $\rho_{He}$ is tied to a light string of length $L.$ The string is tied to the ground forming an "inverted" simple pendulum (figure). If the balloon is displaced slightly from equilibrium as in figure and released, the period of the motion is. Take the density of air to be $\rho_{air}$. Assume the air applies a buoyant force on the balloon but does not otherwise affect its motion.

If the length of a pendulum is made $9$ times and the mass of the bob is made $4$ times,then the value of the time period becomes:

The sum of kinetic energy and potential energy of a simple pendulum bob is $0.02 \text{ J}$. The speed of the simple pendulum bob at the equilibrium position is approximately: (Consider mass of the bob = $20 \text{ g}$) (in $\text{ m/s}$)

$T_{0}$ is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to $\frac{1}{16}$ times its initial value,the modified time period will be:

If a simple pendulum is taken to a place where $g$ decreases by $2\%$,then the time period: