A cylinder rolls down two different inclined | vedclass

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

Question

(D) For a cylinder rolling down an inclined plane of height $h$,the mechanical energy is conserved. The potential energy at the top is converted into

Vedclass · Accepted Answer

The speed will be same but time of descent will be different.

Vedclass · Answer

(D) For a cylinder rolling down an inclined plane of height $h$,the mechanical energy is conserved. The potential energy at the top is converted into translational and rotational kinetic energy at the bottom: $mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$. Since $I = \frac{1}{2}mr^2$ and $v = r\omega$,we have $mgh = \frac{1}{2}mv^2 + \frac{1}{2}(\frac{1}{2}mr^2)(\frac{v}{r})^2 = \frac{3}{4}mv^2$. Thus,$v = \sqrt{\frac{4gh}{3}}$. Since $h$ is the same,the final speed $v$ is the same in both cases.The acceleration of a body rolling down an incline is $a = \frac{g \sin 	heta}{1 + \frac{I}{mr^2}}$. Since the inclination $	heta$ is different,the acceleration $a$ will be different. The time of descent is given by $t = \sqrt{\frac{2s}{a}}$,where $s = \frac{h}{\sin 	heta}$. Substituting $a$,we get $t = \sqrt{\frac{2h}{g \sin^2 	heta} (1 + \frac{I}{mr^2})}$. Since $	heta$ is different,the time of descent $t$ will be different. Therefore,the speed is the same,but the time of descent is different.

$A$ cylinder rolls down two different inclined planes of the same height but of different inclinations.

Similar Questions

$A$ solid sphere rolls without slipping on an inclined plane at an angle $\theta$. The ratio of total kinetic energy to its rotational kinetic energy is

$A$ solid sphere is rolling without slipping on a horizontal rough surface and starts rising on an inclined rough surface as shown in the figure. Assume pure rolling throughout the motion. Choose the $INCORRECT$ statement.

What is the velocity of a sphere starting from rest and rolling without slipping down an inclined plane of vertical height $h$?

$A$ 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?

Vedclass Test Series

Exam Paper Generator

Online Exam Module