$A$ simple pendulum is suspended from the ceiling of a lift. When the lift is at rest,its period is $T$. With what acceleration $a$ should the lift be accelerated upward in order to reduce the period to $\frac{T}{2}$? (Take $g$ as the acceleration due to gravity.)

The velocity of a simple pendulum is maximum at

$A$ simple pendulum of length $2 \ m$ is given a horizontal push through an angular displacement of $60^{\circ}$. If the mass of the bob is $200 \ g$,the angular velocity of the bob will be (Take acceleration due to gravity $g = 10 \ m/s^2$).

$A$ man measures the time period of a pendulum $(T)$ in a stationary lift. If the lift moves upward with an acceleration of $\frac{g}{4}$,then the new time period will be:

$A$ 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?

$A$ $50 \ cm$ long simple pendulum is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration $\sqrt{3} \ g \ m/s^2$. The time period of small oscillations of the pendulum about its equilibrium position is $.... \ s$ $\left(g=\pi^2 \ m/s^2\right):-$