A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4 \mathrm{~m}$, then the time period of small oscillations will be ____ $s$. $\left[\right.$ take $\left.\mathrm{g}=\pi^2 \mathrm{~ms}^{-2}\right]$

A simple pendulum of frequency $f$ has a metal bob. If bob is charged negatively and is allowed to oscillate with large positive charged plate under it, frequency will be

Can simple pendulum clock be used in an artificial satellite ? Why ?

Two pendulums begins to swing simultaneously. The first pendulum makes $11$ full oscillations when the other makes $9$. The ratio of length of the two pendulums is

A simple pendulum has time period $T_1$. The point of suspension is now moved upward according to equation $y = k{t^2}$ where $k = 1\,m/se{c^2}$. If new time period is $T_2$ then ratio $\frac{{T_1^2}}{{T_2^2}}$ will be