There was an Assertion/Reason in our last test at coaching. I am still confused on it!

**Statement 1:** If a disc of radius \(\frac{R}{2}\) rolls in a circular ring of radius R without slipping then all particles on circumference of disc moves on straight lines. (Ring is fixed)

**Statement 2:**Angular velocity of disc and the angular velocity of centre of the disc wrt centre of ring are equal.

A) Statement 1 is false and Statement 2 is true.

B) Satement 1 is true and Statement 2 is false.

C) Both are true, and Statement 2 **explains** Statement 1.

D) Both are true, but Statement 2 **does not explains** Statement 1.

*Thats quite obvious that statement two is wrong as angular velocities being vectors in opposite direction cannot be equal. Can someone explain how statement 1 is correct?*

## Comments

Sort by:

TopNewestHere is the solution.

Image

Log in to reply

Here is an excellent article on discs rolling inside rings of various sizes. Scroll down to the discussion regarding a disc of half the radius of the ring to find three diverse proofs of statement 1. Sorry for 'being lazy' and just providing a link, but since an explanation is greatly enhanced by the inclusion of diagrams I felt this was the appropriate thing to do. – Brian Charlesworth · 2 years, 9 months ago

Log in to reply

– Pranjal Jain · 2 years, 9 months ago

Yeah! Ok thanks! Lemme check it out!Log in to reply