Two bodies of different masses $m_1$ and $m_2$ have equal momenta. Their kinetic energies $E_1$ and $E_2$ are in the ratio:

Match the items in Column-$I$ with Column-$II$.

Column-$I$	Column-$II$
$(1)$ Work done is zero	$(a)$ By gravitational force (when body moves down)
$(2)$ Work done is positive	$(b)$ Against gravitational force (when body moves up)
$(3)$ Work done is negative	$(c)$ By centripetal force

$A$ 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 ...... $ms^{-1}$.

$A$ free body of mass $8 \, kg$ is travelling at $2 \, m/s$ in a straight line. At a certain instant,the body splits into two equal parts due to an internal explosion which releases $16 \, J$ of energy. Neither part leaves the original line of motion. Finally:

$A$ particle of mass $m = 2 \ kg$ is initially at rest. The force $(F)$ versus displacement $(x)$ graph is shown in the figure.
$(1)$ The speed of the particle will be maximum at $x = ..... \ m$.
$(2)$ The maximum speed of the particle is ...... $ms^{-1}$.
$(3)$ The speed of the particle will be zero again at $x = .... \ m$.

Two bodies $A$ and $B$ of masses $2m$ and $m$ are projected vertically upwards from the ground with velocities $u$ and $2u$ respectively. The ratio of the kinetic energy of body $A$ and the potential energy of body $B$ at a height equal to half of the maximum height reached by body $A$ is (in $ : 1$)