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 $N$):

$A$ motor drives a body along a straight line with a constant force. The power $P$ developed by the motor must vary with time $t$ according to

$A$ body of mass $5\,kg$ is moving with a momentum of $10\,kg\,m/s$. Now a force of $2\,N$ acts on the body in the direction of its motion for $5\,s$. The increase in the kinetic energy of the body is $...........J$.

$A$ bullet of mass $m_1$ is moving with speed $v_0$ and hits a sand bag of mass $m_2$. If the speed of the bullet after passing through the sand bag is $\frac{v_0}{3}$,then the height $h$ up to which the bag rises is (assume,$g=$ acceleration due to gravity).

$A$ $70\, kg$ man leaps vertically into the air from a crouching position. To take the leap,the man pushes the ground with a constant force $F$ to raise himself. The center of gravity rises by $0.5\, m$ before he leaves the ground. After the leap,the center of gravity rises by another $1\, m$. The maximum power delivered by the muscles is: (Take $g = 10\, ms^{-2}$)

Two bodies moving towards each other collide and move away in opposite directions. There is some rise in temperature of bodies because a part of the kinetic energy is converted into