Embibe Experts Solutions for Chapter: Rotational Mechanics, Exercise 1: Assam CEE 2016

The mass of a solid circular disc is $500 \mathrm{g}$, the circumference is $3.14 \mathrm{m}$ and thickness is $5 \mathrm{mm}$. The moment of Inertia of the disc about an axis tangential to the rim and perpendicular to the plane of rotation is

A small object of uniform density rolls up a curved surface with an initial velocity $v$. It reaches up to a maximum height of $\frac{3v^2}{4g}$ with respect to the initial position. The object is 

Consider three circular discs each with radius $R$ and mass $M$. The first disc has uniform mass per unit area, the second disc has a mass per unit area $\propto r$ and the third disc has a mass per unit area $\propto \frac{1}{r}$. Here, $r$ is the distance from the centre of the disc. Which of these discs has the lowest moment of inertia about an axis passing through the centre and perpendicular to the plane of the disc? (Or in other words, which of the discs is the easiest to rotate about the given axis?)

The rope of a kite is wound around a hollow cylinder of mass $200 \mathrm{g}$ and radius $5 \mathrm{cm}$. If the kite experiences a pull of $F=1 \mathrm{N}$, what will be the linear acceleration of the rope?

The velocity of a solid sphere on reaching the bottom of an inclined plane is $v$ when it rolls down and $v^{\text{'}}$ when it slides down. The value of $\frac{v}{v^{\text{'}}}$ will be,

A solid cylinder of mass $m$ and radius $r$ rolls without slipping down an inclined plane of length $l$ and height $h$. The speed of its centre of mass when the cylinder reaches the bottom is,

A particle of mass $m$ is projected with a velocity $v$ making an angle of $45°$ with the horizontal. The magnitude of angular momentum of the projectile about an axis of projection when the particle is at maximum height $h$ is,