Two men of masses $80 \mathrm{kg}$ and $60 \mathrm{kg}$ are standing on a wooden plank of mass $100 \mathrm{kg}$ that has been placed over a smooth surface. If both the men start moving towards each other with speeds $1 \mathrm{m} {\mathrm{s}}^{-1}$ and $2 \mathrm{m} {\mathrm{s}}^{-1}$, respectively, the velocity of the plank by which it starts moving is,

A block of mass, $m_1=2\mathrm{kg}$ slides on a frictionless table with speed of  $10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$. In front of it, another block of mass $m_2=5\mathrm{kg}$ is moving with speed $3\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ in the same direction and a massless spring of spring constant, $k=1120\mathrm{ }\mathrm{N} {\mathrm{m}}^{-1}$ is attached on the backside of $m_2$ as shown. The maximum compression of the spring in $\mathrm{cm}$ when the blocks collide is,

A man is standing on a cart of mass which is double the mass of the man. Initially, the cart is at rest on the smooth ground. Now, the man jumps with relative velocity $v$, horizontally towards right with respect to the cart. The work done by the man during the process of jumping is,

A block of mass $2m$ is kept on a smooth circular track of mass $m$ which is kept on a smooth horizontal surface. The circular track is given a horizontal velocity $\sqrt{2gR}$, towards left and is released. The maximum height reached by $2m$ will be,

A block of mass $M=2 \mathrm{kg}$, with a semicircular track of radius $R=1.1 \mathrm{m}$, rests on a horizontal frictionless surface. A uniform cylinder of radius $r=0.1 \mathrm{m}$ and mass $m=1.0 \mathrm{kg}$ is released from rest from the top point $A$. The cylinder slips on the semicircular frictionless track. The speed of the block when the cylinder reaches the bottom of the track at $B$ is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A person $P$ of mass $50\mathrm{ }\mathrm{kg}$ stands in the middle of a boat of mass $100\mathrm{ }\mathrm{kg}$ moving at a constant velocity $10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-1}$ with no friction between water and boat and also the engine of the boat is shut off. With what velocity (relative to the boat surface) should the person move so that the boat comes to rest. Neglect friction between water and boat.

A cannon shell, moving along a straight-line, bursts into two parts. Just after the burst, one part moves with momentum $40 \mathrm{N} \mathrm{s}$, making an angle $30°$ with the original line of motion. The minimum momentum of the other part of the shell just after the burst is,

A man and a plank of the same mass are moving together with a velocity $v$ along the positive $x$-axis. At some instant of time, the man jumps along the negative axis with a velocity $v$ with respect to ground. Then, the speed of the plank after the jump is,