If a second's pendulum is moved to a planet where the acceleration due to gravity is $4$ times that on Earth,the length of the second's pendulum on the planet should be made .......... times to keep the time period constant.

$A$ bob of mass $m$ suspended by a thread of length $l$ undergoes simple harmonic oscillations with time period $T$. If the bob is immersed in a liquid that has density $1/4$ times that of the bob and the length of the thread is increased by $1/3$ of the original length,then the time period of the simple harmonic oscillations will be :-

$A$ string of a pendulum of length $l$ is displaced through $90^{\circ}$ from its vertical and released. Then,the minimum strength of the string needed to withstand the tension as the pendulum passes through its mean position is

$A$ child is sitting on a swing which performs $S.H.M$. It has minimum and maximum heights from the ground of $0.75 \,m$ and $2 \,m$ respectively. Its maximum speed will be $\left[g=10 \,m/s^2\right]$

$A$ 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

$A$ pendulum clock that keeps correct time on the earth is taken to the moon. It will run (given that $g_{Moon} = g_{Earth}/6$):