Embibe Experts Solutions for Chapter: Centre of Mass, Momentum and Collisions, Exercise 1: Exercise 1

Initially two stable particles x and y start moving towards each other under mutual attraction. If at one time the velocities of x and y are V and 2V respectively, what will be the velocity of centre of mass of the system?

A 2 kg body and a 3 kg body are moving along the x-axis. At a particular instant the 2 kg body has a velocity of 3 m/s and the 3 kg body has the velocity of 2 m/s. The velocity of the centre of mass at that instant is :-

A bullet of mass $10 \mathrm{g}$ moving with $300 \mathrm{m} {\mathrm{s}}^{-1}$ hits a block of ice of mass $5 \mathrm{kg}$ and drops dead. The velocity of ice is

A block of mass $m$ rests on a rough horizontal surface (Coefficient of friction is $\mu$). When a bullet of mass $\frac{m}{2}$ strikes horizontally, and get embedded in it, the block moves a distance $d$ before coming to rest. The initial velocity of the bullet is $k\sqrt{2\mu gd}$, then the value of $k$ is

A force of $50$ dynes is acted on a body of mass $5 \mathrm{g}$ which is at rest for an interval of $3 \mathrm{s},$ then impulse is

A ball weighing $10 \mathrm{g}$ hits a hard surface vertically with a speed of  $5 \mathrm{m} {\mathrm{s}}^{-1}$ and rebounds with the same speed. The ball remains in contact with the surface for $0.01 \mathrm{s}$. The average force exerted by the surface on ball is,

A glass ball A of mass $50 \mathrm{g}$ moving with a velocity of $3 \mathrm{m} {\mathrm{s}}^{-1}$ along $x$-axis hits another ball $B$ of mass $50 \mathrm{g}$ which is initially at rest (consider the collision as a perfect elastic collision). The velocities of the two balls after collision are

Read the passage and answer the following question:

In all types of collision, the linear momentum is conserved but kinetic energy is not conserved in inelastic collision. Two bodies of equal masses interchange their velocities after elastic collision. If after collision, two bodies stick together and move as one body with same velocity, the collision is called inelastic collision.

In elastic collision