The acceleration due to gravity at a place is $\pi^2 \, m/s^2$. Then the time period of a simple pendulum of length $1 \, m$ is:

The graph between the time period $(T)$ and the length $(l)$ of a simple pendulum is

If the metal bob of a simple pendulum is replaced by a wooden bob, then its time period will

$A$ 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.

$A$ simple pendulum of length $L$ is constructed from a point object of mass $m$ suspended by a massless string attached to a fixed pivot point. $A$ small peg is placed at a distance $2L/3$ directly below the fixed pivot point so that the pendulum would swing as shown in the figure. The mass is displaced $5$ degrees from the vertical and released. How long does it take to return to its starting position?

Choose the correct length $(L)$ versus square of time period $(T^2)$ graph for a simple pendulum executing simple harmonic motion.