Embibe Experts Solutions for Chapter: Rotational Mechanics, Exercise 5: BEGINNER'S BOX - 5

Two gear wheels which are meshed together have radii of $0.50 \mathrm{cm}$ and $0.15 \mathrm{cm}$. The number of revolutions undergone by the smaller one when the larger goes through $3 \mathrm{revolutions}$ is:

A uniform circular disc of mass $200 \mathrm{g}$ and radius, $4 \mathrm{cm}$ is rotated about one diameter at an angular speed of, $10 \mathrm{rad} {\mathrm{s}}^{-1}$. Find the kinetic energy of the disc and its angular momentum about the axis of rotation.

The angular velocity of a body changes from ${\omega }_1$ to ${\omega }_2$ without applying external torque. Then find the ratio of initial radius of gyration to final radius of gyration.

A stone is attached to a string and is revolved in a circular path with constant angular velocity $\omega$. In this state its angular momentum is $L$. If the length of the string is reduced to half, and again it is revolved with the same angular velocity $\omega$ then find its angular momentum.

A thin uniform thin rod of mass $m$ and length $l$ is suspended from one of its ends and is rotated at the rate of $f$ rotations per second. Find the rotational kinetic energy of the rod.

A wheel of the moment of inertia $10 \mathrm{kg} {\mathrm{m}}^2$ rotates at the rate of $10$ revolutions per minute. Find the work done in increasing its speed to $5$ times of its initial value.

A solid ball of mass $1 \mathrm{kg}$ and radius $3 \mathrm{cm}$ is rotating about its own axis with an angular velocity of $50 \mathrm{rad} {\sec }^{-1}$. Find its kinetic energy of rotation.

When sand is poured gradually on the edge of a rotating disc, what will be the change in its angular velocity?