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

Two bodies of masses $m_{1}$ and $m_{2}$ are acted upon by a constant force $F$ for a time $t$. They start from rest and acquire kinetic energies,$E_{1}$ and $E_{2}$ respectively. Then $\frac{E_{1}}{E_{2}}$ is

The block starts from rest as shown in the figure. Find the work done by the force of $10 \,N$ and friction in the time $0$ to $4 \,s$. [Take, $g=10 \,m/s^2$]

$A$ spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $2.0 \,N \,m^{-1}$ and the mass of the block is $2.0 \,kg$. Ignore the mass of the spring. Initially, the spring is in an unstretched condition. Another block of mass $1.0 \,kg$ moving with a speed of $2.0 \,m \,s^{-1}$ collides elastically with the first block. The collision is such that the $2.0 \,kg$ block does not hit the wall. The distance, in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is. . . .

Which one of the following statements does not hold true when two balls of masses $m_1$ and $m_2$ undergo an elastic collision?

Two spheres $S_1$ and $S_2$ of masses $m_1$ and $m_2$ respectively collide with each other. Initially, $S_1$ is at rest and $S_2$ is moving with velocity $v$ along the $x$-axis. After the collision, $S_2$ has a velocity $\frac{v}{2}$ in a direction perpendicular to the original direction. The sphere $S_1$ moves after the collision: