Embibe Experts Solutions for Chapter: Rotational Mechanics, Exercise 6: BEGINNER'S BOX - 6

The moment of inertia of a wheel about its axis of rotation is $3.0 \mathrm{MKS}$ units. Its kinetic energy is $600 \mathrm{J}$. Find its period of rotation.

The moment of inertia of a wheel is $1000 \mathrm{kg} {\mathrm{m}}^2$. At a given instant, its angular velocity is $10 \mathrm{rad} {\mathrm{s}}^{-1}$. After the wheel rotates through an angle of $100 \mathrm{rad}$, its angular velocity increases to $100 \mathrm{rad} {\mathrm{s}}^{-1}$. Calculate the torque applied on the wheel.  

The moment of inertia of a wheel is $1000 \mathrm{kg} {\mathrm{m}}^2$. At a given instant, its angular velocity is $10 \mathrm{rad} {\mathrm{s}}^{-1}$. After the wheel rotates through an angle of $100 \mathrm{rad}$, its angular velocity increases to $100 \mathrm{rad} {\mathrm{s}}^{-1}$. Calculate the torque applied on the wheel.

A ring, a disc and a solid sphere are simultaneously released to roll down from the top of a rough inclined plane of height $h$. Write the order in which these three bodies will reach the bottom?

A hollow cylinder is rolling down an inclined plane which is inclined at an angle of ${30}^{\circ }$ to the horizontal. Find its speed after travelling a distance of $10 \mathrm{m}$.