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 $4\,m/sec$. There is a constant frictional force of $500\, N$. The work done by the lifting mechanism is

A uniform chain (mass $M,$ length $L$) is released from rest from a smooth horizontal surface as shown in the figure. Velocity of the chain at the instant it completely comes out of the table will be

The potential energy of a particle oscillating along $x-$ axis  is given as $U = 20 + (x - 2)^2$  where $U$  is in joules and $x$ in $meters$ . Total mechanical energy of the particle is $36\,\, J$ . Maximum kinetic energy of the particle is ................ $\mathrm{J}$

A cricket ball of mass $0.15\, kg$ is thrown vertically up by a bowling machine so that it rises to a maximum height of $20 \;m$ after leaving the machine. If the part pushing the ball applies a constant force $F$ on the ball and moves horizontally a distance of $0.2\, m$ while launching the ball, the value of $F($ in $N)$ is 

$\left(g=10\, m s^{-2}\right)$

A body of mass $0.5\; kg$ travels in a stratght line with velocity $v=a x^{3 / 2}$ where $a=5\; m ^{-1 / 2} s ^{-1}$ What is the work done (in $J$) by the net force during its displacement from $x=0$ to $x=2\; m ?$

$STATEMENT$-$1$ A block of mass $\mathrm{m}$ starts moving on a rough horizontal surface with a velocity $\mathrm{v}$. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of $30^{\circ}$ with the horizontal and the same block is made to go up on the surface with the same initial velocity $v$. The decrease in the mechanical energy in the second situation is smaller than that in the first situation. because

$STATEMENT$- $2$ The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.