Embibe Experts Solutions for Chapter: Rotational Mechanics, Exercise 1: TS EAMCET - 5 August 2021 Shift 1

A long slender rod is welded to a thin circular disc of diameter $0.5 \mathrm{m}$ at a point on its circumference. The rod is in the same plane as that of the disc and forms a tangent to the disc. The radius of gyration of the disc about the rod (in $m$) is

A rigid body of mass $M$ and radius $R$ rolls without slipping on an inclined plane of inclination $\theta ,$ under gravity. Match the type of body Column I with magnitude of the force of friction Column II.

If the earth shrinks to $\frac{1}{8}$ of its original volume, while maintaining the same mass, then the duration of the day will be

A circular hoop of radius $50 \mathrm{cm}$ and mass $1 \mathrm{kg}$ rotating with an angular velocity ${\omega }_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. Let $\text{'}v\text{'}$ be the velocity of the centre of the hoop when it ceases to slip. The ratio $v/{\omega }_0$ will be

A thin uniform rod of mass $1 \mathrm{kg}$ and length $1 \mathrm{m}$ is hanged at one end to the ground floor. It originally stands vertically and is allowed to fall to the ground. If the rod hits the ground with angular speed $\omega$ then the correct statement is (Assume $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A solid sphere of radius $R$ makes a perfect rolling down on a plane which is inclined to the horizontal axis at an angle $\theta$. If the radius of gyration is $k$, then its acceleration is

A small disc of mass $500 \mathrm{gm}$ and radius $5 \mathrm{cm}$ rolls down an inclined plane without slipping. Speed of its center of mass when it reaches the bottom of the incline plane depends on

Three bodies a ring, a solid cylinder and a solid sphere roll down an inclined plane without slipping. They start from rest. Which of the bodies reaches bottom of plane with minimum velocity?