$A$ 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

In a simple pendulum,the period of oscillation $T$ is related to the length of the pendulum $l$ as

$A$ 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.)

$A$ second's pendulum is placed in a space laboratory orbiting around the earth at a height $3R$,where $R$ is the radius of the earth. The time period of the pendulum is

$A$ hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom, the period of oscillation will

$A$ simple pendulum of length $l$ is made to oscillate with an amplitude of $45^{\circ}$. The acceleration due to gravity is $g$. Let $T_0 = 2 \pi \sqrt{l / g}$. The time period of oscillation of this pendulum will be