Three bodies,a ring,a solid cylinder,and a so | vedclass

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

Question

(C) We assume the conservation of energy of the rolling body,i.e.,there is no loss of energy due to friction. The potential energy lost by the body in

Vedclass · Accepted Answer

Solid sphere

Vedclass · Answer

(C) We assume the conservation of energy of the rolling body,i.e.,there is no loss of energy due to friction. The potential energy lost by the body in rolling down the inclined plane $(=mgh)$ must be equal to the kinetic energy gained. Since the bodies start from rest,the kinetic energy gained is equal to the final kinetic energy of the bodies.The total kinetic energy $K$ of a body rolling without slipping is given by $K = \frac{1}{2}mv^2(1 + \frac{k^2}{R^2})$,where $v$ is the final velocity of the center of mass,$k$ is the radius of gyration,and $R$ is the radius.Equating $K$ and $mgh$:$mgh = \frac{1}{2}mv^2(1 + \frac{k^2}{R^2})$$v^2 = \frac{2gh}{1 + k^2/R^2}$$v = \sqrt{\frac{2gh}{1 + k^2/R^2}}$For a ring,$k^2 = R^2$:$v_{	ext{ring}} = \sqrt{\frac{2gh}{1 + 1}} = \sqrt{gh}$For a solid cylinder,$k^2 = R^2/2$:$v_{	ext{cylinder}} = \sqrt{\frac{2gh}{1 + 1/2}} = \sqrt{\frac{4gh}{3}}$For a solid sphere,$k^2 = 2R^2/5$:$v_{	ext{sphere}} = \sqrt{\frac{2gh}{1 + 2/5}} = \sqrt{\frac{10gh}{7}}$Comparing the velocities:$v_{	ext{ring}} = \sqrt{1.00gh}$$v_{	ext{cylinder}} = \sqrt{1.33gh}$$v_{	ext{sphere}} = \sqrt{1.43gh}$Thus,the solid sphere reaches the ground with the maximum velocity.

Three bodies,a ring,a solid cylinder,and a solid sphere,roll down the same inclined plane without slipping. They start from rest. The radii of the bodies are identical. Which of the bodies reaches the ground with maximum velocity?

Similar Questions

In the hardening stage of plaster of Paris,the compound formed is:

Male cockroach can be identified from the female by the presence of

The number of real solutions of $\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^2+x+1}=\frac{\pi}{2}$ is

Which series possesses an inferior ovary?

Vedclass Test Series

Exam Paper Generator

Online Exam Module