A simple pendulum of length $L$ oscillates with a time period $T$. If the bob is replaced with another bob of mass four times the original, and the amplitude is halved, the new time period will be:

If a simple pendulum of length l has maximum angular displacement θ, then the maximum kinetic energy of bob of mass m is

A simple pendulum is suspended from the roof of a trolley which moves in a horizontal direction with an acceleration a, then the time period is given by $T = 2\pi \sqrt {\frac{1}{{g'}}}$ where ${g'}$ is equal to

A pendulum clock that shows correct time on the surface of earth is taken to the surface of moon where ${g_{{\rm{moon}}}} = \frac{{{g_{{\rm{earth}}}}}}{6}$. The clock will run

The bob of a simple pendulum of length L is released at time $t{\rm{ }} = {\rm{ }}0$ from a position of small angular displacement. Its linear displacement at time t is given by

A particle executes harmonic motion with an angular velocity and maximum acceleration of $3.5\;\,\,rad/s$ and $\;7.5\,\,m/{s^2}$ respectively. The amplitude of oscillation is

Two simple pendulums, A and B, have lengths $l$ and $4l$ respectively. If the time period of pendulum A is T, what is the time period of pendulum B?

Two pendulums of lengths 484 cm and 400 cm start vibrating together. How many oscillations will the shorter pendulum complete before they are again in phase at the mean position?

Two simple pendulums of lengths 144 cm and 100 cm are initially in phase. After what minimum number of oscillations of the shorter pendulum will they both return to the in-phase condition at their mean positions?

If the mass of the sun were ten times smaller and the universal gravitational constant were ten times larger inmagnitude, which of the following is not correct ?

Two pendulums have lengths of 1.21 m and 1.00 m and start vibrating in phase. After how many vibrations of the shorter pendulum will they next be in phase at their mean positions?