A disc of radius 1,m and mass 4,kg rolls on a | vedclass

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

Question

(A) Given:Radius $R = 1\,m$Mass $M = 4\,kg$Linear velocity $v = 10\,cm/s = 0.1\,m/s$For a disc rolling without slipping,the moment of inertia about th

Vedclass · Accepted Answer

$0.01$

Vedclass · Answer

(A) Given:Radius $R = 1\,m$Mass $M = 4\,kg$Linear velocity $v = 10\,cm/s = 0.1\,m/s$For a disc rolling without slipping,the moment of inertia about the central axis is $I = \frac{1}{2}MR^2$.The angular velocity is $\omega = \frac{v}{R}$.Rotational kinetic energy $K_{rot} = \frac{1}{2}I\omega^2$.Substituting $I = \frac{1}{2}MR^2$ and $\omega = \frac{v}{R}$:$K_{rot} = \frac{1}{2} \left( \frac{1}{2}MR^2 ight) \left( \frac{v}{R} ight)^2 = \frac{1}{4}Mv^2$.$K_{rot} = \frac{1}{4} 	imes 4\,kg 	imes (0.1\,m/s)^2 = 1 	imes 0.01 = 0.01\,J$.

$A$ disc of radius $1\,m$ and mass $4\,kg$ rolls on a horizontal plane without slipping in such a way that its centre of mass moves with a speed of $10\,cm/s$. Its rotational kinetic energy is (in $,J$)

Similar Questions

$A$ sphere rolls without slipping. The radius of gyration about an axis passing through its center of mass is $K$. If the radius of the sphere is $R$,what fraction of the total energy is in the form of rotational kinetic energy?

$A$ symmetrical body of mass $M$ and radius $R$ is rolling without slipping on a horizontal surface with linear speed $v$. Then its angular speed is

$A$ disc rolls without slipping with a constant velocity. What fraction of its total kinetic energy is in the form of rotational kinetic energy?

$A$ thin circular ring and a circular disc of equal mass are rolling without sliding. If their linear velocities are equal and the total kinetic energy of the disc is $6 \ J$,then the total kinetic energy of the ring is (in $J$)

$A$ circular disc is rolling on a horizontal plane. Its total kinetic energy is $300 \, J$. The translational kinetic energy of the disc is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module