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:

The period of simple pendulum is measured as $T$ in a stationary lift. If the lift moves upwards with an acceleration of $5\, g$, the period will be

A pendulum bob has a speed of $3\, {m} / {s}$ at its lowest position. The pendulum is $50 \,{cm}$ long. The speed of bob, when the length makes an angle of $60^{\circ}$ to the vertical will be $ …….\,{m} / {s}$ $\left(g=10 \,{m} / {s}^{2}\right)$

Write the laws of simple pendulum.

There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is $T$. If the resultant acceleration becomes $g/4,$ then the new time period of the pendulum is