Law of Conservation of Linear Momentum

A man of $60 \mathrm{kg}$ is running on the road and suddenly jumps into a stationary trolly car of mass $120 \mathrm{kg}$. Then the trolly car starts moving with velocity $2{ \mathrm{m} \mathrm{s}}^{-1}$. The velocity of the running man was _____ $\mathrm{m} {\mathrm{s}}^{-1}$, when he jumps into the car.

A block moving horizontally on a smooth surface with a speed of $40{ \mathrm{m} \mathrm{s}}^{-1}$ splits into two equal parts. If one of the parts moves at $60{ \mathrm{m} \mathrm{s}}^{-1}$ in the same direction, then the fractional change in the kinetic energy will be $x: 4$ where $x=$ ________.

A block moving horizontally on a smooth surface with a speed of $40 \mathrm{m} {\mathrm{s}}^{-1}$ splits into two parts with masses in the ratio of $1 : 2.$ If the smaller part moves at $60 \mathrm{m} {\mathrm{s}}^{-1}$ in the same direction, then the fractional change in kinetic energy is :

A ball of mass $10 \mathrm{kg}$ moving with a velocity $10\sqrt{3}{ \mathrm{m} \mathrm{s}}^{-1}$ along $X$-axis, hits another ball of mass $20 \mathrm{kg}$ which is at rest. After the collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along $Y$-axis at a speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$. The second piece starts moving at a speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle $\theta$ (degree) with respect to the $X$-axis. The configuration of pieces after the collision is shown in the figure. The value of $\theta$(in degrees) to the nearest integer is _________.

A ball of mass $10 \mathrm{kg}$ moving with a velocity $10\sqrt{3} \mathrm{m} {\mathrm{s}}^{-1}$ along the $x$ -axis, hits another ball of mass $20 \mathrm{kg}$ which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along $y$ -axis with a speed of $10 \mathrm{m} {\mathrm{s}}^{-1}.$ The second piece starts moving at an angle of $30°$ with respect to the $x$ -axis. The velocity of the ball moving at $30°$ with $x$ -axis is $x \mathrm{m} {\mathrm{s}}^{-1}.$ The configuration of pieces after the collision is shown in the figure below. The value of $x$ to the nearest integer is

An object of mass ${\mathrm{m}}_1$ collides with another object of mass ${\mathrm{m}}_2$, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses ${\mathrm{m}}_2:{\mathrm{m}}_1$ is :

Given the masses of various atomic particles ${\mathrm{m}}_{\mathrm{P}}=1,0072\mathrm{u}$, ${\mathrm{m}}_{\mathrm{n}}=1,0087\mathrm{u}$, ${\mathrm{m}}_{\mathrm{e}}=0.000548\mathrm{u}$, ${\mathrm{m}}_{\overline{\mathrm{v}}}=0$, ${\mathrm{m}}_{\mathrm{d}}=2.0141\mathrm{u}$, where $\mathrm{p}=$proton, $\mathrm{n}\equiv$neutron, $\mathrm{e}\equiv$electron, $\overline{\mathrm{v}}\equiv$antineutrino and $\overline{\mathrm{d}}\equiv$deuteron. Which of the following process is allowed by momentum and energy conservation :

A block of mass $\mathrm{m}=1 \mathrm{kg}$ slides with velocity $\mathrm{v}=6 \mathrm{m} {\mathrm{s}}^{-1}$ on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about $\mathrm{O}$ and swings as a result of the collision making angle $\theta$ before momentarily coming to rest. if the rod has mass $M=2 \mathrm{kg},$ and length $\ell =1 \mathrm{m},$ the value of $\theta$ is approximately$\left.(\mathrm{take} \mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become ƒA. The value of ƒ is:

A man (mass $=50\mathrm{k}\mathrm{g}$ ) and his son (mass $=20\mathrm{k}\mathrm{g}$ ) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of $0.70\mathrm{m}\mathrm{ }{\mathrm{s}}^{-1}$ with respect to the man. The speed of the man with respect to the surface is: