I am confused!! Someone help me out??

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?

Note by Pranjal Jain
6 years, 8 months ago

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Here is the solution.

Image

- 6 years, 7 months ago

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.

- 6 years, 8 months ago

Yeah! Ok thanks! Lemme check it out!

- 6 years, 8 months ago