An object of mass $3 \,kg$ is tied by a string of negligible mass to a ceiling and held such that the string is taut. The object is released suddenly such that the string remains taut. Its acceleration when released is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,ms^{-2}$)

$A$ man with a wrist watch and a pendulum clock rises to the top of a $TV$ tower. Both the wrist watch and the pendulum clock accidentally fall from the top of the tower. Then:

The velocity of a simple pendulum is maximum at

$A$ mass falls from a height $h$ and its time of fall $t$ is recorded in terms of time period $T$ of a simple pendulum. On the surface of the Earth,it is found that $t = 2T$. The entire setup is taken to the surface of another planet whose mass is half that of the Earth and radius is the same. The same experiment is repeated and corresponding times are noted as $t'$ and $T'$.

$A$ simple pendulum has a time period $t$. Its time period in a lift which is moving upwards with an acceleration of $3 \ m/s^2$ is:

$A$ simple pendulum of length $L$ has mass $M$ and it oscillates freely with amplitude $A$. At the extreme position,its potential energy is: