Question

A uniform circular ring rolls without slipping on a horizontal surface, At any instant its position is as shown in the figure.Then

• A. section $ABC$ has greater kinetic energy than section $ADC$
• B. section $BC$ has greater kinetic energy than section $CD$
• C. section $BC$ has the same kinetic energy as section $DA$
• D. the sections $CD$ and $DA$ have the same kinetic energy

Answer 1

Answer: (A), (B), (D)

The correct options are
A section $ABC$ has greater kinetic energy than section $ADC$
B section $BC$ has greater kinetic energy than section $CD$
D the sections $CD$ and $DA$ have the same kinetic energy

For a body undergoing pure rolling about ground with no slip, the point of contact has zero velocity and thus the body seems to rotate about that point. Hence, speed of any point on the body at given distance 'r' from point of contact is same. speed(P) = rW , where W=angular velocity.

So, upper two quadrants of the ring are radially symmetric about O and hence have same speed distribution among particles. So, do their kinetic energy.

Similarly, for the bottom two too.

But, bottom two quadrant will have lower speed as they are nearer to O.