If a second's pendulum is moved to a planet where the acceleration due to gravity is $4$ times that on Earth,the length of the second's pendulum on the planet should be made .......... times to keep the time period constant.

$A$ pendulum bob is swinging in a vertical plane such that its angular amplitude is less than $90^o$. At its highest point,the string is cut. Which trajectory is possible for the bob afterwards?

Two light strings,each of length $\ell$,are fixed at points $A$ and $B$ on a fixed horizontal rod $xy$. $A$ small bob is tied by both strings and is in equilibrium,the strings are making an angle of $45^{\circ}$ with the rod. If the bob is slightly displaced normal to the plane of the strings and released,then the period of the resulting small oscillation will be:

$A$ simple pendulum is taken to a place where its distance from the Earth's surface is equal to the radius of the Earth. Calculate the time period of small oscillations if the length of the string is $4.0 \ m$. (Take $g = \pi^2 \ m/s^2$ at the surface of the Earth.) (in $s$)

If a simple pendulum is taken to a place where $g$ decreases by $4\%$,then the time period

The time period of a simple pendulum is $T$. When the length is increased by $10 \ cm$, its period is $T_1$. When the length is decreased by $10 \ cm$, its period is $T_2$. Then, the relation between $T, T_1$, and $T_2$ is