Two identical discs of same radius `R` are rotating about their axes in opposite directions with the same constant angular speed `omega` . The discs are in the same horizontal plane. At time `t = 0` , the points `P` and `Q` are facing each other as shown in the figure. The relative speed between the two points `P` and `Q` is `v_(r)`. In one time period `(T) ` of rotation of the discs , `v_(r)` as a function of time is best represented by

Options

A.
B.
C.
D.

Answer

A

Explanation

AT an instatnt, speed of ` P=v`, going in clockwese direction
Speed of ` Q = v`, going in anticlokwise direction Relative andgular velocity of ` P w.r.t. Q = omega - (-omega)`
`=2 omega`
Relative angular separation of ` P` and ` Q` in time (t)
` theta = 2 omega t`.
Relative speed between the points ` P` and ` Q` at time (t)`
` | vec _r | = sqrt (v^2+vec v^2 - 2 vv cos (2 omega t))`
` =2 v is omega t`
Since, ` | vec_r|` will not have any negative value so the lower part of the sine wave will come upper siede. Hence option (a) is true.