$A$ 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 $\left[g=10 \,m/s^2\right]$

The height of a swing changes during its motion from $0.1\, m$ to $2.5\, m$. The minimum velocity of a boy who swings in this swing is ..... $m/s$.

In a seconds pendulum,the mass of the bob is $30\, g$. If it is replaced by a $90\, g$ mass,then its time period will be .... $s$.

$A$ person of mass $M$ is sitting on a swing of length $L$ and swinging with an angular amplitude $\theta_0$. If the person stands up when the swing passes through its lowest point,the work done by him,assuming that his centre of mass moves by a distance $l$ $(l << L)$,is close to

$A$ pendulum suspended from the ceiling of a train has a period $T$ when the train is at rest. When the train travels the same distance per unit time,the period of oscillation is

If $R$ is the radius of the earth and the acceleration due to gravity on the surface of the earth is $g = \pi^2 \ m/s^2$,then the length of the second's pendulum at a height $h = 2R$ from the surface of the earth will be: