Embibe Experts Solutions for Chapter: Centre of Mass, Momentum and Collisions, Exercise 5: Exercise (Previous Year Questions)

For inelastic collision between two spherical rigid bodies

Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant, then the speed of centre of mass of system will be

A man of $50 \mathrm{kg}$ mass is standing in a gravity free space at a height of $10 \mathrm{m}$ above the floor. He throws a stone of $0.5 \mathrm{kg}$ mass downwards with a speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$. When the stone reaches the floor, the distance of the man above the floor will be.

On a frictionless surface, a block of mass $M$ moving at speed $v$ collides elastically with another block of same mass $M$ which is initially at rest. After collision, the first block moves at an angle $\mathrm{\theta }$ to its initial direction and has a speed $\frac{v}{3}$. The second block's speed after the collision is 

A bullet of mass $10 \mathrm{g}$ moving horizontally with a velocity of $400 {\mathrm{ms}}^{-1}$  strikes a wooden block of mass $2 \mathrm{kg}$ which is suspended by a light inextensible string of length $5 \mathrm{m}$ . As a result, the centre of gravity of the block found to rise a vertical distance of $10 \mathrm{cm}$ . The speed of the bullet after it emerges out horizontally from the block will be

A moving block having mass $m,$ collides with another stationary block having mass $4m.$ The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v$, then the value of the coefficient of restitution $\left(e\right)$ will be

The total mass of the cart is $2$ metric tons in which $1$ metric tons of sand is loaded. The system is initially at rest. The sand leaks out of the cart (from the hole at the bottom) at the rate of $0.5 \mathrm{kg} {\mathrm{s}}^{-1}$ and an external horizontal force of $10 \mathrm{N}$ is acting on it. The final velocity of the cart when the sand completely leaks out is

A solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane of length $L$ and height $h$. What is the speed of its centre of mass when the cylinder reaches its bottom?