A solid cylinder of mass M and radius R rolls | vedclass

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

Question

(A) For a solid cylinder rolling down an inclined plane,the total energy at the top is potential energy $PE = Mgh$. At the bottom,the total energy is

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) For a solid cylinder rolling down an inclined plane,the total energy at the top is potential energy $PE = Mgh$. At the bottom,the total energy is the sum of translational kinetic energy and rotational kinetic energy: $KE = \frac{1}{2} Mv^2 + \frac{1}{2} I\omega^2$. For a solid cylinder,the moment of inertia $I = \frac{1}{2} MR^2$ and the rolling condition is $v = R\omega$,so $\omega = \frac{v}{R}$. Substituting these into the energy equation: $Mgh = \frac{1}{2} Mv^2 + \frac{1}{2} (\frac{1}{2} MR^2) (\frac{v}{R})^2$. $Mgh = \frac{1}{2} Mv^2 + \frac{1}{4} Mv^2$. $Mgh = \frac{3}{4} Mv^2$. Solving for height $h$: $h = \frac{3 v^2}{4 g}$.

$A$ solid cylinder of mass $M$ and radius $R$ rolls down a smooth inclined plane about its own axis and reaches the bottom with velocity $v$. What is the height of the inclined plane? (Assume $g$ is the acceleration due to gravity.)

Similar Questions

$A$ solid cylinder and a hollow cylinder,both of the same mass and same external diameter,are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

$A$ disc rolls without slipping down an inclined plane of length $L$ and inclination $\theta$. What will be its velocity at the bottom?

$A$ uniform ring of radius $R$ is moving on a horizontal surface with speed $v$,then climbs up a ramp of inclination $30^{\circ}$ to a height $h$. There is no slipping in the entire motion. Then,$h$ is

$A$ solid cylinder of mass $M$ and radius $R$ rolls down an inclined plane without slipping. The speed of its centre of mass when it reaches the bottom is ...

Vedclass Test Series

Exam Paper Generator

Online Exam Module