A solid sphere of mass 1 kg rolls on a table | vedclass

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

Question

(C) The total kinetic energy $(K)$ of a rolling body is the sum of its translational kinetic energy $(K_t)$ and rotational kinetic energy $(K_r)$.$K =

Vedclass · Accepted Answer

$0.7$

Vedclass · Answer

(C) The total kinetic energy $(K)$ of a rolling body is the sum of its translational kinetic energy $(K_t)$ and rotational kinetic energy $(K_r)$.$K = K_t + K_r = \frac{1}{2} M v^2 + \frac{1}{2} I \omega^2$For a solid sphere,the moment of inertia about its center is $I = \frac{2}{5} M R^2$ and the angular velocity is $\omega = \frac{v}{R}$.Substituting these values:$K = \frac{1}{2} M v^2 + \frac{1}{2} (\frac{2}{5} M R^2) (\frac{v}{R})^2$$K = \frac{1}{2} M v^2 + \frac{1}{5} M v^2$$K = (\frac{1}{2} + \frac{1}{5}) M v^2 = \frac{7}{10} M v^2$Given $M = 1 \ kg$ and $v = 1 \ m/s$:$K = \frac{7}{10} 	imes 1 	imes (1)^2 = 0.7 \ J$.

$A$ solid sphere of mass $1 \ kg$ rolls on a table with linear speed $1 \ m/s$. Its total kinetic energy is .......... $J$.

Similar Questions

Given $V_{CM} = 2\; m/s$,$m = 2\; kg$,$R = 4\; m$. Find the angular momentum of the ring about the origin if it is in pure rolling. (in $kg \cdot m^2/s$)

$A$ spherical ball is rolling on a table without slipping. What fraction of its total kinetic energy is associated with its rotational motion?

Consider a cylinder of mass $M$ resting on a rough horizontal rug that is pulled out from under it with acceleration $a$ perpendicular to the axis of the cylinder. What is the friction force $F_{friction}$ at point $P$? It is assumed that the cylinder does not slip.

$A$ uniform solid sphere of mass $m$ and radius $R$ is being pulled on a horizontal surface with a force $F$ parallel to the surface,applied at its topmost point. If the acceleration of the center of mass of the sphere is $a$ and it is rolling without slipping on the surface,the value of $F$ is:

$A$ hoop of radius $2 \; m$ weighs $100 \; kg$. It rolls along a horizontal floor so that its centre of mass has a speed of $20 \; cm/s$. How much work has to be done to stop it?

Vedclass Test Series

Exam Paper Generator

Online Exam Module