A thin disc and a thin ring, both have mass M and radius R. Both rotate about axes through their centre of mass and are perpendicular to their surfaces at the same angular velocity. Which of the following is correct?

examrobotsa's picture

Submitted by examrobotsa on

Q: (NDA-II/2019)
A thin disc and a thin ring, both have mass M and radius R. Both rotate about axes through their centre of mass and are perpendicular to their surfaces at the same angular velocity.
Which of the following is correct?

question_subject: 

Science

question_exam: 

NDA-II

stats: 

0,6,6,6,2,3,1

keywords: 

{'thin ring': [0, 0, 0, 1], 'thin disc': [0, 0, 0, 1], 'same kinetic energy': [0, 0, 0, 1], 'same angular velocity': [0, 0, 0, 1], 'kinetic energies': [0, 0, 0, 4], 'higher kinetic energy': [0, 0, 0, 1], 'ring': [4, 0, 2, 6], 'disc': [1, 0, 1, 4], 'axes': [0, 0, 0, 1], 'surfaces': [0, 0, 1, 2], 'mass': [0, 0, 2, 3]}

The correct answer is option 1: The ring has higher kinetic energy.

To understand why this is the case, let`s compare the moments of inertia of the disc and the ring. The moment of inertia is a measure of an object`s resistance to changes in rotational motion and is given by the formula I = 1/2 * m * r^2, where m is the mass and r is the radius of the object.

For a thin disc, the moment of inertia is I = 1/2 * M * R^2.

For a thin ring, the moment of inertia is I = M * R^2.

Since the moment of inertia of the ring is greater than the moment of inertia of the disc, we can conclude that the ring has more resistance to changes in rotational motion. In other words, it takes more energy to set the ring into motion compared to the disc.

Since both objects are rotating at the same angular velocity, it means that they both have the same kinetic energy per unit of mass. However, since the ring has a higher moment of inertia, it will require more mass to achieve the same angular velocity as the disc. Therefore, the ring has a higher total kinetic energy compared to the disc.

In summary, option 1 is