Embibe Experts Solutions for Chapter: Rotational Motion, Exercise 1: Exercise 1

A force $\overrightarrow{\mathrm{F}}=\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}-5\hat{\mathrm{k}}\right) \mathrm{N}$ acts at a point ${\overrightarrow{\mathrm{r}}}_1=(2\hat{\mathrm{i}}+4\hat{\mathrm{j}}+7\hat{\mathrm{k}}) \mathrm{m}.$ The torque of the force about the point ${\overrightarrow{\mathrm{r}}}_2=(\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}}) \mathrm{m}$ is

A wheel of the moment of inertia ${10}^3 \mathrm{kg}{ \mathrm{m}}^2$ is rotating with an angular speed of $5 \mathrm{rad} {\mathrm{s}}^{-1}$ The torque required to stop it in $2 \mathrm{s}$ is, 

An automobile engine develops $100 \mathrm{kW}$ power when rotating with an angular speed of $250 \mathrm{rad} {\mathrm{s}}^{-1}.$ The torque developed by it will be about, 

The angular momentum of a particle performing uniform circular motion is $L.$If the kinetic energy of partical is doubled and frequency is halved, then angular momentum becomes

A thin uniform circular ring is rolling down an inclined plane of inclination $30°$ without slipping. Its linear acceleration along the inclined plane is

A thin circular ring first slips down a smooth incline then rolls down a rough incline of identical geometry from same height. Ratio of time taken in the two motion is

A cylinder rolls down two different inclined planes of the same height but of different inclinations

What is the minimum coefficient of friction for a solid sphere to roll without slipping on an inclined plane of inclination $\theta ?$