Embibe Experts Solutions for Chapter: Centre of Mass, Exercise 1: TS EAMCET - 5 August 2021 Shift 2

A bullet of mass $m$ moving horizontally with speed $v_0$ hits a wooden block of mass $M$ that is suspended from a massless string. The bullet gets lodged into the block and comes into halt. If the block-bullet combine swings to a maximum height $h$ then how much of the initial kinetic energy of the bullet is lost in the collision?

A ball of mass $100 \mathrm{g}$ is dropped at time $t=0.$ A second ball of mass $200 \mathrm{g}$ is dropped from the same point at $t=0.2 \mathrm{s}$. The distance between the center of mass of two balls and the release point at $t=0.4 \mathrm{s}$ is: (Assume $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A ball of mass $M$ moving with a speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$ hits another ball of mass $1 \mathrm{kg}$ moving in the same direction with a speed of $1 \mathrm{m} {\mathrm{s}}^{-1}$. If the kinetic energy of center of mass is $\frac{4}{3} \mathrm{Joule}$, then the magnitude of $M$ is

An object $A$ of mass $20 \mathrm{kg}$ and travelling at $20 \mathrm{m} {\mathrm{s}}^{-1}$ crashes into another object $B$ of mass $200 \mathrm{kg}$ and travelling at $10 \mathrm{m} {\mathrm{s}}^{-1},$ in the same direction. After the collision, object $A$ bounces back in opposite direction at a speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$. The speed of the object $B$ after the collision is

A particle of mass $m_1$ collides with a particle of $m_2$ at rest. After the elastic collision, the two particles moves at an angle of $90°$ with respect to each other. The ratio $\frac{m_2}{m_1}$ is

Assertion (A): When we bounce a ball on the ground, it comes to rest after a few bounces, losing all its energy. This is an example of violation of conservation of energy.

Reason (R): Energy can change from one form to another but the total energy is always conserved.

Which of the following is true?

A ball of mass $1 \mathrm{kg}$ moving along $X$-direction collides elastically with a stationary ball of mass $m$. The first ball (mass $=1 \mathrm{kg}$) recoils at right angle to its original direction of motion. If the second ball starts moving at an angle $30°$ with the $X$-axis, the value of $m$must be

Ball $P$ of mass $m$ moving with velocity $\text{'}v\text{'}$ collides with another ball $Q$ of mass $2 \mathrm{m},$ at rest. If $v_P$ and $v_Q$ are the final velocities of $P$ and $Q$ respectively, after collision, then
(Assume the coefficient of restitution is $1/3$)