Two identical discs of same radius R are rota | vedclass

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(A) Let the angular velocity of both discs be $\omega$. The linear velocity of any point on the rim of the disc is $v = R\omega$.At time $t=0$,the poi

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(A) Let the angular velocity of both discs be $\omega$. The linear velocity of any point on the rim of the disc is $v = R\omega$.At time $t=0$,the points $P$ and $Q$ are at the horizontal position facing each other.After time $t$,the points rotate by an angle $	heta = \omega t$.The velocity vector of point $P$ makes an angle $	heta$ with the vertical,and the velocity vector of point $Q$ also makes an angle $	heta$ with the vertical.The horizontal components of the velocities are $v_x(P) = -v \sin 	heta$ and $v_x(Q) = v \sin 	heta$.The relative velocity in the horizontal direction is $v_{rx} = v_x(P) - v_x(Q) = -v \sin 	heta - v \sin 	heta = -2v \sin 	heta$.The vertical components are $v_y(P) = -v \cos 	heta$ and $v_y(Q) = -v \cos 	heta$.The relative velocity in the vertical direction is $v_{ry} = v_y(P) - v_y(Q) = 0$.Thus,the relative speed is $v_r = |v_{rx}| = |-2v \sin \omega t| = 2v \sin \omega t$.At $t=0$,$v_r = 0$. As $t$ increases,$v_r$ increases,reaching a maximum at $\omega t = \pi/2$,and becomes $0$ again at $\omega t = \pi$. This corresponds to the graph shown in Option $A$.

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