$A$ simple pendulum of length $L$ has mass $M$ and it oscillates freely with amplitude $A$. At the extreme position,its potential energy is $(g =$ acceleration due to gravity$)$

$A$ light balloon filled with helium of density $\rho_{He}$ is tied to a long light string of length $l$ and the string is attached to the ground. If the balloon is displaced slightly in the horizontal direction from the equilibrium and released,then:

The time period of a simple pendulum when it is made to oscillate on the surface of the moon:

The length of a seconds pendulum is $1 \,m$ on the earth. If the mass and diameter of a planet are double that of the earth, then the length of the seconds pendulum on the planet will be: (in $\,m$)

Let $l_1$ be the length of a simple pendulum. Its length changes to $l_2$ to increase the periodic time by $20 \%$. The ratio $\frac{l_2}{l_1}$ is:

The time period of a simple pendulum in air is $T$. If the pendulum is immersed in water and executes $SHM$,its time period is $t$. The value of $\frac{T}{t}$ is [density of the bob is $\frac{5000}{3} \ kg \ m^{-3}$ and density of water is $1000 \ kg \ m^{-3}$].