$A$ simple pendulum with an iron bob has a time period $T$. The bob is now immersed in a non-viscous liquid and oscillated. If the density of the liquid is $\frac{1}{12}$th that of iron,then the new time period will be:

$A$ simple pendulum hanging from the ceiling of a stationary lift has a time period $T_1$. When the lift moves downward with constant velocity,the time period is $T_2$,then

$A$ simple pendulum of time period $1\,s$ and length $l$ is hung from a fixed support at $O$. The bob is at a distance $H$ vertically above $A$ on the ground. The amplitude is $\theta_0$. The string snaps at $\theta = \frac{\theta_0}{2}$. Find the time taken by the bob to hit the ground and the distance from $A$ where the bob hits the ground. Assume $\theta_0$ to be small,so that $\sin \theta_0 \approx \theta_0$ and $\cos \theta_0 \approx 1$.

$A$ child is sitting on a swing which performs $S.H.M$. It has minimum and maximum heights from the ground of $0.75 \,m$ and $2 \,m$ respectively. Its maximum speed will be $\left[g=10 \,m/s^2\right]$

The path length of oscillation of a simple pendulum of length $1 \,m$ is $16 \,cm$. Its maximum velocity is (Take $g = \pi^2 \,m/s^2$).

$A$ simple pendulum is suspended in a car. The car starts moving on a horizontal road according to the equation $x = \frac{g}{2} \sqrt{3} t^2$. Find the time period of oscillation of the pendulum.