For a rolling spherical shell,the ratio of ro | vedclass

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

Question

(D) The rotational kinetic energy of a body is given by $K_{	ext{rot}} = \frac{1}{2} I \omega^2$,where $I$ is the moment of inertia and $\omega$ is t

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(D) The rotational kinetic energy of a body is given by $K_{	ext{rot}} = \frac{1}{2} I \omega^2$,where $I$ is the moment of inertia and $\omega$ is the angular velocity.For a spherical shell,the moment of inertia about its center is $I = \frac{2}{3} mR^2$.For pure rolling,$\omega = \frac{v}{R}$,so $K_{	ext{rot}} = \frac{1}{2} (\frac{2}{3} mR^2) (\frac{v}{R})^2 = \frac{1}{3} mv^2$.The total kinetic energy is $K_{	ext{total}} = K_{	ext{trans}} + K_{	ext{rot}} = \frac{1}{2} mv^2 + \frac{1}{3} mv^2 = \frac{5}{6} mv^2$.The ratio of rotational kinetic energy to total kinetic energy is $\frac{K_{	ext{rot}}}{K_{	ext{total}}} = \frac{\frac{1}{3} mv^2}{\frac{5}{6} mv^2} = \frac{1}{3} 	imes \frac{6}{5} = \frac{2}{5}$.Given that the ratio is $\frac{x}{5}$,we have $\frac{x}{5} = \frac{2}{5}$,which implies $x = 2$.

For a rolling spherical shell,the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$. The value of $x$ is ................

Similar Questions

$A$ thin uniform circular disc rolls with a constant velocity without slipping on a horizontal surface. Its total kinetic energy is

Consider a point $P$ at the contact point of a wheel on the ground,which rolls on the ground without slipping. Find the displacement of point $P$ when the wheel completes half of a rotation (given the radius of the wheel is $1 \ m$).

$A$ solid sphere of radius $R$ is rolled by a force $F$ acting at the top of the sphere as shown in the figure. The sphere rolls without slipping on a rough stationary surface. Initially,the sphere is at rest. Then:

When a rolling body enters onto a smooth horizontal surface,it will ............

Vedclass Test Series

Exam Paper Generator

Online Exam Module