Linear Momentum of a System of Particles

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

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 nucleus disintegrates into two nuclear parts which have their velocities in the ratio $2:1$. The ratio of their nuclear sizes will be

A man throws a ball straight up. The ball has a momentum in the vertically upward direction.The principle of conservation of momentum demands that the earth has

Two balls having linear momenta ${\overrightarrow{p}}_1=p\hat{\mathrm{i}}$ and ${\overrightarrow{p}}_2=-p\hat{\mathrm{i}}$, undergo a collision in free space. There is no external force acting on the balls. Let ${\overrightarrow{p}}_1^{\text{'}}$ and ${\overrightarrow{p}}_2^{\text{'}}$ be their final momenta. The following option (s) is (are) not allowed for any non-zero value of $p, a_1, a_2, b_1, b_2, c_1$ and $c_2$.

A man of mass $50 \mathrm{kg}$ is standing at one end of a boat of length $25 \mathrm{m}$ and mass $200 \mathrm{kg}$. He starts running and when he reaches the other end, he has a velocity $2{ \mathrm{ms}}^{-1}$ with respect to the boat. The final velocity of the boat is (in ${\mathrm{ms}}^{-1}$)

A shell of mass $10 \mathrm{kg}$ is moving with a velocity of $10{ \mathrm{m} \mathrm{s}}^{-1}$ when it blasts and forms two parts of mass $9 \mathrm{kg}$ and $1 \mathrm{kg}$ respectively. If the 1st mass is stationary, the velocity of the $2\mathrm{nd}$ is

A ball of mass $0.2 \mathrm{kg}$ rests on a vertical post of height $5 \mathrm{m}$. A bullet of mass $0.01 \mathrm{kg}$, travelling with a velocity $v \mathrm{m}/\mathrm{s}$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of $20 \mathrm{m}$ and the bullet at a distance of $100 \mathrm{m}$ from the foot of the post. The initial velocity $v$ of the bullet is

A shell is fired from a cannon with a velocity $v$ $\left(\mathrm{m} {\mathrm{s}}^{-1}\right)$  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 with speed $v \cos \theta$ then the speed (in $\mathrm{m} {\mathrm{s}}^{-1}$) of the other piece immediately after the explosion is

A $3 \mathrm{kg}$ ball strikes a heavy rigid wall with a speed of $10 \mathrm{m}/\mathrm{s}$ at an angle of $60°$ with the wall. It gets reflected with the same speed at $60°$ as shown in Fig.If the ball is in contact with the wall for $0.2 \mathrm{s}$, the average force on the ball by the wall is:

Ball $1$ collides with another identical ball at rest. For what value of coefficient of restitution $\mathrm{e},$  the velocity of second ball becomes two times that
of $1$ after collision?

A man of mass $80 \mathrm{kg}$ is standing on a cart of mass $100 \mathrm{kg}$ and initially the system is moving with a velocity of $5 \mathrm{m}/\mathrm{s}$ The surface between the ground and the cart is smooth. If the man jumps forwards with a velocity of $15 \mathrm{m}/\mathrm{s}$ with respect to the final motion of the cart, the velocity of the cart will become:

A particle is projected with velocity$\text{'}u\text{'}$ makes an angle $\theta$ w.r.t. horizontal. Now it breaks in two identical parts at highest point of trajectory. If one part retraces its path, then velocity of other part is :-

A stationary bomb explodes into three pieces. One piece of $2 \mathrm{kg}$ mass moves with a velocity of $8 \mathrm{m} {\mathrm{s}}^{-1}$ at right angles to the other piece of mass $1 \mathrm{kg}$ moving with a velocity of $12 \mathrm{m} {\mathrm{s}}^{-1}$. If the mass of the third piece is $0.5 \mathrm{kg}$, then its velocity is:

A $500 \mathrm{kg}$ boat is $9 \mathrm{m}$ long and is floating without motion on still water. A man of mass $100 \mathrm{kg}$ is at one end and if he runs to the other end of the boat and stops, the displacement of the boat is :

A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other, each with a kinetic energy $\frac{E_0}{2}$ . The total energy of explosion is

A bullet of mass $m$ moving with velocity $v$ is fired into a wooden block of mass $M$. If the bullet remains embedded in the block, the final velocity of the system is

$A$ point mass of $1 \mathrm{kg}$ collides elastically with a stationary point mass of $5 \mathrm{kg}$. After their collision, the $1 \mathrm{kg}$ mass reverses its direction and moves with a speed of $2 {\mathrm{ms}}^{-1}.$ Which of the following statements are correct for the system of these two masses?

(A) Total momentum of the system is $3 \mathrm{kg} {\mathrm{ms}}^{-1}$

(B) Momentum of $5 \mathrm{kg}$ mass after collision is $4 \mathrm{kg} {\mathrm{ms}}^{-1}$

(C) Kinetic energy of the centre of mass is $0.75 \mathrm{J}$

(D) Total kinetic energy of the system is $4 \mathrm{J}$

Two blocks $A$ and $B$ are joined together with a compressed spring. When the system is released, the two blocks appear to be moving with unequal speeds in the opposite direction as shown in the figure. Select the correct statement,