If a simple pendulum can reach a height of $10 \ cm$,what is its velocity when it is at its mean position (in $m/s$)? $(g = 9.8 \ m/s^2)$

The time period of a simple pendulum inside a stationary lift is $\sqrt{3} \ s$. When the lift moves upwards with an acceleration $g/3$,the new time period will be ($g=$ acceleration due to gravity).

$A$ pendulum suspended from the ceiling of a train oscillates with a time period $2 \ s$,when the train is accelerating at $10 \ m/s^2$. What will be its time period when the train retards at $10 \ m/s^2$?

For a simple pendulum, the graph of time period $(T)$ versus length $(l)$ is depicted by:

$A$ 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.

$A$ pendulum has a time period $T$. If it is taken to another planet having an acceleration due to gravity half that of the Earth and a mass $9$ times that of the Earth,then its time period on the other planet will be: