$A$ body of mass $5\,kg$ rests on a rough horizontal surface of coefficient of friction $0.2$. The body is pulled through a distance of $10\,m$ by a horizontal force of $25\,N$. The kinetic energy acquired by it is ......... $J$.

$A$ particle is moving in a circle of radius $r$ under the action of a force $F = \alpha r^2$ which is directed towards the centre of the circle. The total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy $= 0$ for $r = 0$).

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 $N$):

The diagram 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 $(R \text{ & } S)$ is minimum at $t = 2 \text{ ms}$.
$(III)$ The mass of $R$ was greater than the mass of $S$.

$A$ body of mass $5\; kg$ is moving with a momentum of $10\; kg\; m/s$. $A$ force of $0.2\; N$ acts on it in the direction of motion of the body for $10\; s$. Find the increase in its kinetic energy. (in $; J$)

$A$ wooden block of mass $M$ is suspended by a cord and is at rest. $A$ bullet of mass $m$,moving with a velocity $v$,passes through the block and emerges with a velocity $v/2$ in the same direction. If the block rises to a height $H$,calculate the value of $H$.