The diagram to the right shows the velocity-time graph for two masses $R$ and $S$ that collided elastically. Which of the following statements is true?

$(I)$ $R$ and $S$ moved in the same direction after the collision.

$(II)$ Kinetic energy of the system $(R$ & $S)$ is minimum at $t = 2$ milli sec.

$(III)$ The mass of $R$ was greater than mass of $S.$

Assume the aerodynamic drag force on a car is proportional to its speed. If the power output from the engine is doubled, then the maximum speed of the car.

Work done by the frictional force is

In one dimensional case, the relationship between force and position is shown in the figure. The work done by the force in displacing a body from $x = 1\, cm$ to $x = 5\, cm$ is ............ $\mathrm{ergs}$

A ball after falling from a height of $10\, m$ strikes the roof of a lift which is descending  down with a velocity of $1\, m/s$. The recoil velocity of the ball will be .............. $\mathrm{m}/ \mathrm{s}$

A particle of mass $m$ moving with velocity $V_0$ strikes a simple pendulum of mass $m$ and sticks to it. The maximum height attained by the pendulum will be