The period of a simple pendulum measured inside a stationary lift is found to be $T$. If the lift starts accelerating upwards with an acceleration of $g/3$,then the time period of the pendulum is

$A$ disc of mass $m$ and radius $R$ is attached to the ceiling with the help of two ropes of length $l$. Find the time period of small oscillations of the disc in the plane of the disc.

$A$ 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.

At a given place, to increase the number of oscillations made by a simple pendulum in one minute from $72$ to $90$, the length of the pendulum is to be decreased by (in $\%$)

In an elevator,a spring clock of time period $T_S$ (mass attached to a spring) and a pendulum clock of time period $T_P$ are kept. If the elevator accelerates upwards,what happens to their time periods?

Savitha, a $XI$ standard student, while conducting an experiment to determine the effective length of a simple pendulum $L$, notes down the data of time taken to complete $30$ oscillations as $60 \text{ s}$ and hence calculates the length of the simple pendulum as: (Take $\pi^2 = 9.8$, and $g = 9.8 \text{ m/s}^2$) (in $\text{ m}$)