Embibe Experts Solutions for Chapter: Centre of Mass, Momentum and Collisions, Exercise 4: Exercise-4

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 is 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 its centre. 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:

A ball collides with an inclined plane of inclination $\mathrm{\theta }$ after falling through a distance $h$. If it moves horizontally just after the impact, the coefficient of restitution is

A plate in the form of a semicircle of radius $r$$a$ has a mass per unit area of $k r$ where$k$ is a constant and $r$ is the distance from the centre of the straight edge. By dividing the plate into semicircular rings, find the distance of the centre of mass of the plate from the centre of its straight edge.
 

A point mass of $1 \mathrm{kg}$ collides elastically with a stationary point mass of $5 \mathrm{kg}$. After their collision, the $1 \mathrm{kg}$ mass reverses its direction and moves with a speed of $2{ \mathrm{m} \mathrm{s}}^{-1}$. Which of the following statement(s) is (are) correct for the system of these two masses?