Assertion : A uniform disc of radius R is performing impure rolling motion on a rough horizontal plane as shown in figur. After some time the disc comes to rest. It is possible only when `v_(0) = (omega_(0)R)/(2)`

Reason : For a body performing pure rolling motion, the angular momentum uis conserved about any point in space.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. If Assertion is true but Reason is fasle
D. If Assertion is false but Reason is true

Answer

C

Explanation

Angular momentum about bottommost point will be
`L=mv_(0)R-(1)/(2)mR^(2)omega_(0)`
If `L=0 or v_(0)=(omega_(0)R)/(2)`, disc will come to rest after some time.