Linear Momentum of a System of Particles

An object of mass $4\text{kg}$ and another object of mass $1\text{kg}$ are moving such that they have equal kinetic energy. The ratio of the magnitudes of their linear momentum is

A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragment with equal masses fly in mutually perpendicular directions with speeds of 21 ms^-1​. The velocity of heaviest fragment in ms^-1 will be

A particle of mass m is projected towards a wall such that the angle of incidence is $\theta$0 and the speed just before collision is$u$. Assuming that the wall is smooth and the collision is elastic, show that the ball rebounds at same angle.

A railway wagon (open at the top) of mass ${\mathrm{M}}_1$ is moving with speed $v_1$ along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes ${\mathrm{M}}_2$ and speed becomes ${\mathrm{v}}_2$. Taking the rain to be falling vertically and water stationary inside the wagon, the relation between the two speeds ${\mathrm{v}}_1$ and ${\mathrm{v}}_2$ is :

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $1:2^{1/3}$. Their respective speed have a ratio of $n:1$. The value of $n$ is_________

A particle of mass $m$ moving with velocity $v$ collides with a stationary particle of mass $2m$. After collision, they stick together and continue to move together with velocity

A bullet of mass $0.1 \mathrm{kg}$ moving horizontally with speed $400 \mathrm{m} {\mathrm{s}}^{-1}$ hits a wooden block of mass $3.9 \mathrm{kg}$ kept on a horizontal rough surface. The bullet gets embedded into the block and moves $20 \mathrm{m}$ before coming to rest. The coefficient of friction between the block and the surface is _______.

A particle of mass $m$ moving with a velocity $v$ collides with a particle of mass $2m$ at rest and sticks to it. Velocity of combined mass is equal to

A sphere of mass $m$ falls on a smooth hemisphere of mass$M$resting with its plane face on smooth horizontal table, so that at the moment of impact, line joining the centres makes an angle $\alpha$ with the vertical. The velocity of sphere just before impact is$u$and $e$ is the coefficient of restitution.

A ball of mass $m$ strikes the fixed inclined plane after falling through a height$h$. If it rebounds elastically, the impulse on the ball is: 

 A man of mass $m$ stands on a long flat car of mass $M$ moving with velocity $V$. If he now begins to run with velocity $u$ with respect to the car, in the same direction as $V,$ the velocity of the car will be:
 

 Block$A$ of mass $1 \mathrm{kg}$ is placed on the rough surface of block$B$ of mass $3 \mathrm{kg}$. Block B is placed on smooth horizontal surface. Blocks are given the velocities as shown. Find net work done by the frictional force. [in $(-) ve$ $\mathrm{J}$]

A body at rest breaks up into 3 parts. If 2 parts having equal masses fly off perpendicularly each after with a velocity of $12 \mathrm{m} {\mathrm{s}}^{-1}$, then the velocity of the third part which has 3 times mass of each part is

Two bodies of masses ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ are dropped from heights ${\mathrm{h}}_1$ and ${\mathrm{h}}_2$ respectively. On reaching the ground, they acquire equal momenta. If ${\mathrm{h}}_1>{\mathrm{h}}_2$, the ratio of kinetic energy of ${\mathrm{m}}_1$ to that of on reaching the ground will be

Two balls A and B having mass $1 \mathrm{kg}$ and $2 \mathrm{kg}$, moving with speed $21$ $\mathrm{m} {\mathrm{s}}^{-1}$and $4 \mathrm{m} {\mathrm{s}}^{-1}$ respectively in opposite direction, collide head on. After collision A moves with a speed of $1 \mathrm{m} {\mathrm{s}}^{-1}$ in the same direction, then the coefficient of restitution is:

 

 Two particles$A$and $B$ of equal masses having initial velocities$V_A= (8\hat{\mathrm{i}} +8\hat{\mathrm{j}}) \mathrm{m} {\mathrm{s}}^{-1}$and $V_B=(\hat{\mathrm{i}}+\hat{\mathrm{j}}) \mathrm{m} {\mathrm{s}}^{-1}$respectively collide. collision is head-on and elastic, then the final velocities of $A$and $B$respectively will be
 

Compare the momentum of two of this of mass $10 \mathrm{kg}$and $40 \mathrm{kg}$ respectively but having the same kinetic energy.

A flat car of mass$\mathrm{M}$ is at rest on a frictionless floor with a child of mass m standing at the edge. If the child jumps off from the car towards right with initial velocity $\mathrm{u}$, with respect to car, find the velocity of car after the jump.
 

A bomb moving with velocity $\left(40 \hat{\mathrm{i}}+50 \hat{\mathrm{j}}-25 \hat{\mathrm{k}}\right) \mathrm{m} {\mathrm{s}}^{-1}$ explodes into two pieces of mass ratio $1:4$. After explosion the smaller piece moves away with velocity $\left(200 \hat{\mathrm{i}}+70 \hat{\mathrm{j}}+15 \hat{\mathrm{k}}\right) \mathrm{m} {\mathrm{s}}^{-1}$. The velocity of the larger piece is