A solid sphere having mass m and radius r rol | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For a solid sphere rolling without slipping,the moment of inertia is $I = \frac{2}{5}mr^2$ and the condition for rolling is $v = r\omega$,which im

Vedclass · Accepted Answer

$\frac{2}{7}$ rotational and $\frac{5}{7}$ translational

Vedclass · Answer

(B) For a solid sphere rolling without slipping,the moment of inertia is $I = \frac{2}{5}mr^2$ and the condition for rolling is $v = r\omega$,which implies $\omega = \frac{v}{r}$.The rotational kinetic energy is $K_{rot} = \frac{1}{2}I\omega^2 = \frac{1}{2} (\frac{2}{5}mr^2) (\frac{v}{r})^2 = \frac{1}{5}mv^2$.The translational kinetic energy is $K_{trans} = \frac{1}{2}mv^2$.The total kinetic energy is $K_{total} = K_{rot} + K_{trans} = \frac{1}{5}mv^2 + \frac{1}{2}mv^2 = \frac{7}{10}mv^2$.The fraction of rotational kinetic energy is $\frac{K_{rot}}{K_{total}} = \frac{\frac{1}{5}mv^2}{\frac{7}{10}mv^2} = \frac{1}{5} 	imes \frac{10}{7} = \frac{2}{7}$.The fraction of translational kinetic energy is $\frac{K_{trans}}{K_{total}} = \frac{\frac{1}{2}mv^2}{\frac{7}{10}mv^2} = \frac{1}{2} 	imes \frac{10}{7} = \frac{5}{7}$.Thus,the sphere has $\frac{2}{7}$ rotational and $\frac{5}{7}$ translational kinetic energy. Hence,option $(b)$ is correct.

$A$ solid sphere having mass $m$ and radius $r$ rolls down an inclined plane. Then its kinetic energy is

Similar Questions

$A$ solid cylinder of diameter $30 \ cm$ is rolled down an inclined plane from a height of $2 \ m$. If there is no energy loss due to friction,the angular velocity at the base of the plane is ....... $rad/s$. (Take $g = 10 \ m/s^2$)

$A$ solid sphere rolls down without slipping on a $30^{\circ}$ inclined plane. If $g = 10\,m/s^2$,the acceleration of the rolling sphere is

$A$ uniform spherical object of mass $M$ and radius $R$ has a moment of inertia $I$. It rolls without slipping down an inclined plane of angle $\theta$. What is its acceleration?

$A$ uniform ring of radius $R$ is moving on a horizontal surface with speed $v$,then climbs up a ramp of inclination $30^{\circ}$ to a height $h$. There is no slipping in the entire motion. Then,$h$ is

$A$ solid cylinder and a disc of same radii are allowed to roll down a rough inclined plane from the top of a plane. The ratio of their times taken to reach the bottom of the inclined plane is

Vedclass Test Series

Exam Paper Generator

Online Exam Module