A disc of mass M and radius R rolls on a hori | vedclass

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

Question

(B) The total kinetic energy of a rolling disc is the sum of its translational and rotational kinetic energies.Total Kinetic Energy $K = K_{	ext{tran

Vedclass · Accepted Answer

$\frac{3v^2}{4g}$

Vedclass · Answer

(B) The total kinetic energy of a rolling disc is the sum of its translational and rotational kinetic energies.Total Kinetic Energy $K = K_{	ext{trans}} + K_{	ext{rot}} = \frac{1}{2} Mv^2 + \frac{1}{2} I\omega^2$.For a disc,the moment of inertia $I = \frac{1}{2} MR^2$ and for pure rolling,$\omega = \frac{v}{R}$.Substituting these values,$K = \frac{1}{2} Mv^2 + \frac{1}{2} (\frac{1}{2} MR^2) (\frac{v}{R})^2 = \frac{1}{2} Mv^2 + \frac{1}{4} Mv^2 = \frac{3}{4} Mv^2$.As the disc rolls up the incline,its kinetic energy is converted into gravitational potential energy $Mgh$.By the law of conservation of energy,$\frac{3}{4} Mv^2 = Mgh$.Solving for $h$,we get $h = \frac{3v^2}{4g}$.

$A$ disc of mass $M$ and radius $R$ rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is $v,$ the height to which the disc will rise will be

Similar Questions

$A$ body rolls down an inclined plane without slipping. The kinetic energy of rotation is $50 \%$ of its translational kinetic energy. The body is :

Which of the following (assuming mass and radius are the same) has the maximum percentage of total $K.E.$ in rotational form during pure rolling?

$A$ solid sphere rolls down from rest on an inclined plane. At the same time,a rectangular block slides down from rest on the same inclined plane. Which of the following is true?

$A$ solid cylinder rolls down an inclined plane from a height $h$. At any moment,the ratio of rotational kinetic energy to the total kinetic energy is:

$A$ solid sphere of mass $0.1\,kg$ and radius $2\,cm$ rolls down an inclined plane $1.4\,m$ in length (slope $1$ in $10$). Starting from rest,its final velocity will be .......... $m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module