$A$ child swings on a swing such that the minimum and maximum heights from the ground are $0.75 \ m$ and $2 \ m$ respectively. The maximum velocity of the swing is ...... $ms^{-1}$.

Write the similarity between various forms of energy.

$A$ simple pendulum of length $1 \ m$ has a bob of mass $1 \ kg$. $A$ bullet of mass $10^{-2} \ kg$ is fired into the bob with a speed of $2 \times 10^2 \ m/s$. The bullet gets embedded in the bob. Find the height $h$ to which the bob rises before it swings back. (in $m$)

$A$ bullet of mass $4\,g$ is fired horizontally with a speed of $300\,m/s$ into a $0.8\,kg$ block of wood at rest on a table. If the coefficient of friction between the block and the table is $0.3$,how far will the block slide approximately (in $,m$)?

As shown below, bob $A$ of a pendulum having a massless string of length $R$ is released from $60^{\circ}$ to the vertical. It hits another bob $B$ of half the mass that is at rest on a frictionless table in the center. Assuming an elastic collision, the magnitude of the velocity of bob $A$ after the collision will be (take $g$ as acceleration due to gravity):

Two identical balls $A$ and $B$ are released from the positions shown in the figure. They collide elastically on the horizontal portion $MN$. All surfaces are smooth. The ratio of the maximum heights attained by $A$ and $B$ after the collision will be (Neglect energy loss at $M$ and $N$):