If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length,then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ is

$A$ simple pendulum with length $L$ and mass $m$ of the bob is vibrating with an amplitude $A$. The maximum tension in the string is

At a given place, to increase the number of oscillations made by a simple pendulum in one minute from $72$ to $90$, the length of the pendulum is to be decreased by (in $\%$)

$A$ simple pendulum consisting of a ball of mass $m$ tied to a thread of length $l$ is made to swing on a circular arc of angle $\theta$ in a vertical plane. At the end of this arc,another ball of mass $m$ is placed at rest. The momentum transferred to this ball at rest by the swinging ball is

$A$ simple pendulum is attached to the roof of a lift. If the time period of oscillation when the lift is stationary is $T$,then the frequency of oscillation when the lift falls freely will be

$A$ simple pendulum is suspended from the ceiling of a lift. When the lift is at rest,its time period is $T$. With what acceleration should the lift be accelerated upwards in order to reduce its period to $T/2$ (in $g$)? ($g$ is acceleration due to gravity).