Law of Conservation of Linear Momentum

Three particles $A, B$ and $C$ of equal mass move with equal speed $v$ along the medians of an equilateral triangle as shown in figure. They collide at the centroid $G$ of the triangle. After the collision, $A$ comes to rest, $B$ retraces its path with the speed $V$. What is the velocity of $C$?

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 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 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:

 

In figure, a series of $n$ identical balls is shown on a smooth horizontal surface. If number $1$ moves horizontally with speed $v$ into number $2$ which in turn collides with number $3$, etc. and if the coefficient of restitution for each impact is $e=3/4$, the speed of the $nth$ ball is $(\frac{f}{8}{)}^{n-1}v$
Then $f$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
 

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

Two identical block $A$ and $B$ each of mass $m$ are placed on a smooth horizontal plane. At $t=0$ block $B$ is given a velocity of $5 \mathrm{m} {\mathrm{s}}^{-1}$. Calculate the compression in the spring when velocity of $A$ is $3 \mathrm{m} {\mathrm{s}}^{-1}$, given spring constant of ideal spring is $k$.

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In the shown figure, a particle of mass $\frac{M}{10}$ strikes the block of mass $M$ with velocity $v_0$ and gets attached to it. For what velocity $v_0$ (in $\mathrm{m} {\mathrm{s}}^{-1}$), the block $B$ just able to leave the ground?
(Given $M=100 \mathrm{gm}, \mathrm{K}=880 \mathrm{N} {\mathrm{m}}^{-1}$)

A shell is fired from a cannon with velocity $v \mathrm{m} {\mathrm{s}}^{-1}$ at an angle $\theta$ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed in $\mathrm{m} {\mathrm{s}}^{-1}$ of the other piece immediately after the explosion is,