$A$ simple pendulum has a time period $T$. The bob is given a negative charge and the surface below it is given a positive charge. The new time period will be

$A$ seconds pendulum is placed in a space laboratory orbiting round the Earth at a height $3R$ from the Earth's surface. The time period of the pendulum will be ($R =$ radius of Earth).

$A$ pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is $20 \; m/s^2$ at a distance of $5 \; m$ from the mean position. The time period of oscillation is

$A$ person measures a time period of a simple pendulum inside a stationary lift and finds it to be $T$. If the lift starts accelerating upwards with an acceleration $\left(\frac{g}{3}\right)$,the time period of the pendulum will be

Two pendulums of length $121 \ cm$ and $100 \ cm$ start vibrating in phase. At some instant,the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is:

If the length of the oscillating simple pendulum is made $\frac{1}{3}$ times the original, keeping the amplitude the same, then the increase in its total energy at a place will be: (in $times$)