A disc of radius `R` is spun to an angualr speed `omega_(0)` about its axis and then imparted a horizontal velocity of magnitude `(omega_(0)R)/(4)`. The coefficient of friction is `mu`. The sense of rotation and direction of linear velocity are shown in the figure. The disc will return to its initial position.

Options

A. if the value of `mult0.5`
B. irrespective of the value of `mu`
C. if the value of `0.5ltmult1`
D. if `mugt1`

Explanation

About bottommost point
angular momentum
`L=I_(C)omega_(0)-mv_(0)R` (anticlockwise)
`=(1)/(2)mR^(2)omega-m(omega_(0)(R)/(4))R`

`=(1)/(4)mR^(2)omega_(0)`
`=+` ve or anticlockwise
during slip friction acts about bottommost point. So, its torque is zero or angular momentum about bottommost point should also remain anticlockwise when pure rolling starts. so, figure should be as shown below.
so, the disc will return to its initial position for all value of `mu`.