Embibe Experts Solutions for Chapter: Center of Mass, Momentum and Collision, Exercise 1: Exercise 1

A uniform square plate $ABCD$ has a mass of $10 \mathrm{kg}.$ If two point masses of $3 \mathrm{kg}$ each are placed corners $C$ and $D$ as shown in the adjoining figure, then the centre of mass shifts to the point which lies on -

A bomb of mass $12 \mathrm{kg}$ at rest explodes into two fragments of masses in the ratio $1:3$. The kinetic energy of the smaller fragment is $216 \mathrm{J}$. The momentum of the heavier fragment is (in $\mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$)

A body of mass $(4 \mathrm{m})$ is lying in $\mathrm{x}-\mathrm{y}$. plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass $\left(\mathrm{m}\right)$ move perpendicular to each other with equal speeds $\left(\mathrm{v}\right)$. The total kinetic energy generated due to explosion is
 

A hemisphere of mass $3 \mathrm{m}$ and radius $R$ is free to slide with its base on a smooth horizontal table. A particle of mass $m$ is placed on the top of the hemisphere. If the particle is displaced with a negligible velocity, then find the angular velocity of the particle relative to the centre of the hemisphere at an angular displacement $\mathrm{\theta },$ when the velocity of the hemisphere is $v$.

A point mass $M$ moving with a certain velocity collides with a stationary point mass $M/2$. The collision is elastic and in one-dimension. Let the ratio of the final velocities of $M$ and $M/2$ be $x$. The value of $x$ is

A heavy elevator is moving upwards with constant velocity $5 \mathrm{m} {\mathrm{s}}^{-1}$. At time $t=0$, a ball situated at a distance of $100 \mathrm{m}$ from the elevator is dropped. Find the velocity of the ball just after the collision(elastic) $($use $\left.g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$.

In the figure shown, coefficient of restitution between $A$ and $B$ is $e=\frac{1}{2},$ then

A ball $A$ of mass $M$ collides elastically with another identical ball $B$ at rest as shown in the figure. Initially, velocity of the ball $A$ is $u \mathrm{m} {\mathrm{s}}^{-1}\text{.}$ After collision