Duration: 6:55

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Consider a disc rotating in the horizontal plane with a constant angular speed \( \omega \) about its centre \( O \). The disc has a
\( \mathrm{P} \) shaded region on one side of the diameter and an unshaded

W region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles \( P \) and \( Q \) are simultaneously projected at an angle towards \( R \). The velocity of projection is in the \( y-z \) plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed \( \frac{1}{8} \) rotation. (ii) their range is less than half the disc radius, and (iii) \( \omega \) remains constant throughout. Then [IIT JEE 2012]
(a) \( P \) lands in the shaded region and \( Q \) in the unshaded region
(b) \( P \) lands in the unshaded region and \( Q \) in the shaded region
(c) Both \( P \) and \( Q \) land in the unshaded region
(d) Both \( P \) and \( Q \) land in the shaded region
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