A bullet of mass $10 \;g$ leaves a rifle at an initial velocity of $1000 \;m/s$ and strikes the earth at the same level with a velocity of $500\; m / s$. The work done ($Joule$) in joule overcoming the resistance of air will be

A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses $0.36 \mathrm{~kg}$ and $0.72 \mathrm{~kg}$. Taking $g=10 \mathrm{~m} / \mathrm{s}^2$, find the work done (in joules) by the string on the block of mass $0.36 \mathrm{~kg}$ during the first second after the system is released from rest.

A wedge of mass $M = 4\,m$ lies on a frictionless plane. A particle of mass $m$ approaches the wedge with speed $v$. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by

If a particle of mass $m$ is moving in a horizontal circle of radius $r$ with a centripetal force $( - k/{r^2})$, the total energy is

$STATEMENT$-$1$ 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.

A force acts on a $3 \,gm$ particle in such a way that the position of the particle as a function of time is given by $x = 3t - 4{t^2} + {t^3}$, where $x$ is in metres and $t$ is in seconds. The work done during the first $4 \,seconds$ is ..... $mJ$