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 instant, speed of `P = v`, going in clockwise direction Speed of `Q = v`, going in anticlockwise direction Relative angular velocity of `P w.r.t Q = omega - (- omega) = 2 omega` Relative angualr separation of `P` and `Q` in time `t theta = 2 omegat`. Relative speed between the points `P` and `Q` at time `t` `\| overset rarr(upsilon_(r ))\| = sqrt(upsilon^(2) + upsilon^(2) - 2 upsilon upsilon cos (2 omegat))` `= sqrt(2 upsilon^(2) (1-cos 2 omegat)) = sqrt(2 upsilon^(2) xx 2 sin^(2) omegat)` `= 2 upsilon sin omega t` Since `\| overset rarr(upsilon_(r ))\|` will not have negative value so the lower part of the sine wave will come upper side. Hence option (a) is true.

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