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 A. B. C. D.

Two identical discs of same radius `R` are rotating about their axes i

1.	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 A. B. C. D.
Answer» Correct Answer - A 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.

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