Embibe Experts Solutions for Chapter: Centre of Mass, Momentum and Collisions, Exercise 2: Exercise - 2

A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other, each with the same $\mathrm{KE}, E_0.$ The minimum energy of explosion will be,

Three identical balls of mass m and radius $R$ are placed on frictionless horizontal $\mathrm{x}-\mathrm{y}\text{ plane.}$ Ball $A$ at$(0, 0),$ Ball $B$ at $(\sqrt{ 2} R, –\sqrt{ 2} R).$Ball $A$ is suddenly given an impulse $\overrightarrow{P}=\sqrt{2}mV\hat{\mathrm{i}} .$ If collision between balls $A \text{and} B$ is perfectly elastic while between $B\text{ and }C$ is head on and perfectly inelastic, then.

A projectile is thrown horizontally from top of a tower of height$20 \mathrm{m}$with a velocity $10 \mathrm{m}/\sec .$ It strikes the smooth ground whose co-efficient of restitution is$0.5. [\mathrm{g} = 10 \mathrm{m}/{\mathrm{s}}^2]$ (neglect friction):

Two balls$\mathrm{A} \mathrm{and} \mathrm{B}$moving in the same direction collide. The mass of $\mathrm{B}$ is$\mathrm{p}$ times that of $\mathrm{A}.$Before the collision the velocity of $\mathrm{A}$ was $\mathrm{q}$times that of $\mathrm{B}.$ After the collision $\mathrm{A}$ comes to rest. If $\mathrm{e}$ be the coefficient of restitution then which of the following conclusion/s is/are correct ?

A particle is attached to the lower end of a uniform rod which is hinged at its other end as shown in the figure. The minimum speed given to the particle so that the rod performs circular motion in a vertical plane will be [length of the rod is $l$, consider masses of both rod and particle to be same]

A rod of negligible mass and length $l$ is pivoted at the point $\frac{l}{4}$ distance from the left end as shown. A particle of mass $m$ is fixed to its left end and another particle of mass $2m$ is fixed to the right end. If the system is released from rest and after some time becomes vertical, the speed $v$ of the two masses and angular velocity at that instant is 

Two identical balls $A$ and $B$ of mass $m$ each is placed on a fixed wedge as shown in the figure. The ball $B$ is kept at rest and it is released just before two balls collide. The ball $A$ rolls down without slipping on an inclined plane and collides elastically with the ball $B$. The kinetic energy of the ball $A$ just after the collision with the ball $B$ is (Neglect friction between $A$ and $B$, also neglect the radius of the balls)

Consider two point masses $m_1$ and $m_2$ connected by a light rigid rod of length $r_0$. The moment of inertia of the system about an axis passing through their centre of mass and perpendicular to the rigid rod is given by