Exams › JEE Main › Physics

Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation is:-

1. The sphere has the greatest and the ring has the least velocity of the centre of mass at the bottom of the inclined plane.
2. The ring has the greatest and the cylinder has the least velocity of the centre of mass at the bottom of the inclined plane.
3. All of them will have same velocity.
4. The cylinder has the greatest and the sphere has the least velocity of the centre of mass at the bottom of the inclined plane.

Correct answer: The sphere has the greatest and the ring has the least velocity of the centre of mass at the bottom of the inclined plane.

Solution

The sphere has the greatest velocity because it has the lowest moment of inertia relative to its mass, allowing it to convert more gravitational potential energy into translational kinetic energy as it rolls down the incline. Conversely, the ring has the highest moment of inertia, resulting in less translational speed at the bottom.

Related JEE Main Physics questions

• A satellite moving through a region of free space collects interplanetary dust that is initially at rest. If the dust is gathered at the rate \(\frac{dM}{dt}=\alpha v\), then the satellite’s acceleration is
• A rocket initially ejects gas from its rear at a mass rate of \(0.1\,\text{kg s}^{-1}\). If the exhaust speed relative to the rocket is \(50\,\text{m s}^{-1}\) and the rocket’s mass is \(2\,\text{kg}\), what is its acceleration in \(\text{m s}^{-2}\)?
• A block of mass \(m\) lies at rest on a frictionless horizontal floor. A uniform rope of mass \(m/3\) has one end attached to the block, and the free end is pulled horizontally by a force \(F\). What is the tension at the midpoint of the rope?
• A block of mass \(m\) is attached to a second block of mass \(M\) by a light spring of spring constant \(k\). Both blocks lie on a frictionless horizontal surface. Initially, the system is at rest and the spring is at its natural length. A constant force \(F\) is then applied to the block of mass \(M\) to pull it. Determine the force exerted by the block of mass \(m\).
• A thin ring of mass $M$ and radius $R$ is spinning about its symmetry axis with angular speed $\omega$. Two identical small masses, each of mass $m$, are then lightly fixed at the two opposite ends of a diameter of the ring. The decrease in kinetic energy is
• A sphere rolls on a surface without slipping. Its radius of gyration about an axis through its centre of mass is $K$, and its radius is $R$. What fraction of the total kinetic energy is due to rotation?

⚔️ Practice JEE Main Physics free + battle 1v1 →