Two identical particles are moving with same velocity $v$ as shown in the figure. If the collision is completely inelastic,then:

$A$ pendulum of length $2 \; m$ consists of a wooden bob of mass $50 \; g$. $A$ bullet of mass $75 \; g$ is fired towards the stationary bob with a speed $v$. The bullet emerges out of the bob with a speed $\frac{v}{3}$ and the bob just completes the vertical circle. The value of $v$ is $\dots \; ms^{-1}$. (if $g = 10 \; m/s^2$)

Consider a rubber ball freely falling from a height $h = 4.9\, m$ on a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Which one of the following graphs represents the velocity as a function of time and the height as a function of time?

Answer the following:
$(a)$ The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burning obtained? The rocket or the atmosphere?
$(b)$ Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet's velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is zero. Why?
$(c)$ An artificial satellite orbiting the earth in a very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance,however small. Why then does its speed increase progressively as it comes closer and closer to the earth?
$(d)$ In Figure $(i)$ the man walks $2\; m$ carrying a mass of $15\; kg$ on his hands. In Figure $(ii)$,he walks the same distance pulling the rope behind him. The rope goes over a pulley,and a mass of $15\; kg$ hangs at its other end. In which case is the work done greater?

Fill in the blanks:
$(a)$ If the momentum of an object is doubled,its kinetic energy becomes ........
$(b)$ For a perfectly inelastic collision,the coefficient of restitution $e$ $=$ .....
$(c)$ An appliance with $1\,kW$ power consumes $1\,kWh$ of energy in ....... time.

Two bodies of masses $m$ and $2m$ are attached to the two ends of an ideal spring. The spring is compressed. The total energy stored in the spring is $60 \ J$. If the spring is released,then: