Law of Conservation of Linear Momentum and Its Applications

A 600 kg rocket is set for a vertical firing. If the exhaust speed is 1000 $m{s}^{-}{}^1,$ the mass of the gas ejected per second to supply the thrust needed to overcome the weight of rocket is :

Block $A$ of mass $m$ and block $B$ of mass $2m$ are placed on a fixed triangular wedge by means of a massless inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45°$ to the horizontal on both sides. The coefficient of friction between block $A$ and the wedge is $\frac{2}{3}$ and that between block $B$ and the wedge is $\frac{1}{3}$. If the system of $A$ and $B$ is released from rest, find the magnitude and direction of the force of friction acting on $A.$

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 shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2:2:1$. If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$, the speed of the third (lighter) fragment is:

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:

Block $A$ of weight $100\mathrm{ }\mathrm{N}$ rests on a frictionless inclined plane of slope angle $30°$ as shown in the figure. A flexible cord attached to $A$ passes over a frictionless pulley and is connected to block $B$ of weight $W$. Find the weight $W$ for which the system is in equilibrium.

A shell of mass $\text{'}m\text{'},$ moving with velocity $\text{'}v\text{'}$  suddenly breaks into two pieces. If one of those parts having mass $m/6$ remains stationary, find the velocity of the other part.

The figure shows a block of mass $M,$ attached to an uncompressed spring of spring constant $k,$ resting on a frictionless surface. A bullet of mass $m,$ travelling with a constant horizontal velocity $v$ hits the block and gets embedded inside. What is the maximum compression of the spring ?

A jeweler is holding a gold chain of uniform mass per unit length hanging vertically just above a weighing scale as shown in the figure. He offers to charge the customer for half of the maximum reading of the scale, after he releases the chain. What percentage more than the actual price does the customer pay if he agrees to the offer?

A bullet in motion hits and gets embeded in a solid block resting on a frictionless table. What is conserved?