Solid and Hollow Cylinder on Inclined Plane – Rankers Physics

Solid and Hollow Cylinder on Inclined Plane

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? (2010 Mains)

Both together only when angle of inclination of plane is $45^{\circ}$
Both together
Hollow cylinder
Solid cylinder

Solution:

The acceleration of a rolling body depends on its moment of inertia ratio $I/mR^2$. The solid cylinder has a smaller moment of inertia ratio ($1/2$) compared to the hollow cylinder ($1$), giving it a higher acceleration and causing it to reach the bottom first.

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Questions

Explore conceptually related problems

1. Assertion (A): The condition of equilibrium for a rigid body is – Translational equilibrium: \( \sum \vec{F} = 0 \) (i.e. sum of all external forces equal to zero). Rotational equilibrium: \( \sum \vec{\tau} = 0 \) (i.e. sum of all external torques equal to zero.) Reason (R): A rigid body must be in equilibrium under the action of two equal and opposite forces.  
2. A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation ($E_{sphere} / E_{cylinder}$) will be: (2016 - II)
3. A particle of mass \(m\) is moving on a circle of radius \(R\) with kinetic energy \(K\). Then angular momentum of particle about centre of circle will be:
4. The moment of the force, $\vec{F} = 4\hat{i} + 5\hat{j} - 6\hat{k}$ at $(2, 0, -3)$, about the point $(2, -2, -2)$ is given by (2018)
5. Assertion (A): If there is no external torque on a body about its centre of mass, then the velocity of the center of mass remains constant. Reason (R): The angular momentum of a system always remains constant.