$A$ $1000\, kg$ elevator rises from rest in the basement to the fourth floor,a distance of $20\, m$. As it passes the fourth floor,its speed is $4\, m/s$. There is a constant frictional force of $500\, N$. The work done by the lifting mechanism is

If a rubber ball falls from a height $h$ and rebounds up to a height of $h/2$,the percentage loss of total energy of the initial system and the velocity of the ball just before it strikes the ground,respectively,are:

$A$ hammer of mass $M$ strikes a nail of mass $m$ with a velocity $20 \ m/s$ into a fixed wall. The nail penetrates into the wall to a depth of $1 \ cm$. The average resistance of the wall to the penetration of the nail is

$A$ free body of mass $8 \, kg$ is travelling at $2 \, m/s$ in a straight line. At a certain instant,the body splits into two equal parts due to an internal explosion which releases $16 \, J$ of energy. Neither part leaves the original line of motion. Finally:

$A$ ball of mass $10\, kg$ moving with a velocity $10 \sqrt{3} \, m/s$ along the $x$-axis,hits another ball of mass $20\, kg$ which is at rest. After the collision,the first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along the $y$-axis with a speed of $10 \, m/s$. The second piece starts moving at an angle of $30^{\circ}$ with respect to the $x$-axis. The velocity of the ball moving at $30^{\circ}$ with the $x$-axis is $x \, m/s$. The configuration of pieces after the collision is shown in the figure. The value of $x$ to the nearest integer is:

$A$ toy of mass $20 \,g$ at rest acquires a velocity $(3 \hat{i}-2 \hat{j}) \,m/s$ in $2 \,s$. The power of the toy is: (in $\,W$)