$A$ simple pendulum hangs from the ceiling of a car. If the car accelerates with a uniform acceleration,the frequency of the simple pendulum will

In an experiment for determining the gravitational acceleration $g$ of a place with the help of a simple pendulum,the measured time period square $(T^2)$ is plotted against the string length $(L)$ of the pendulum as shown in the figure. What is the value of $g$ at the place in $m/s^2$?

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 $\%$)

$A$ 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.

''Motion of a simple pendulum from the mean position for small displacement is a simple harmonic motion'' - Explain this statement.

In a simple pendulum,the period of oscillation $T$ is related to the length of the pendulum $l$ as