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

$A$ body is rolling without slipping on a horizontal plane. If the rotational kinetic energy of the body is $40\%$ of the total kinetic energy,then the body might be:

$A$ thin hollow cylinder,open at both ends,slides without rotating and then rolls without slipping with the same speed. The ratio of kinetic energies in the two cases will be:

$A$ ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is $K$. If the radius of the ball is $R$,then the fraction of total energy associated with its rotational energy is:

$A$ solid sphere of mass $2\,kg$ is making pure rolling on a horizontal surface with kinetic energy $2240\,J$. The velocity of the centre of mass of the sphere will be $..........\,m/s$.

The ratio of the total kinetic energy to the rotational kinetic energy for a rolling disc is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module