Consider a disc rotating in the horizontal plane with a constant … - Vidyadip

MCQ

Consider a disc rotating in the horizontal plane with a constant angular speed $\omega$ about its centre $O$. The disc has a shaded region on one side of the diameter and an unshaded 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 completed $\frac{1}{8}$ rotation. $(ii)$ their range is less than half disc radius, and $(iii)$ $\omega$ remains constant throughout. Then

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
✓
Both $P$ and $Q$ land in the unshaded region
D
Both $P$ and $Q$ land in the shaded region

✓

Answer

Correct option: C.

Both $P$ and $Q$ land in the unshaded region

c
Since distance of particle $P$ from point $O$ is initially decreasing then increasing so, its angular velocity $w$ initially increase then decrease. So, angle swept by $P$ is more than angle swept by disc. So it will fall unshaded portion.

Since distance of particle $Q$ from $O$ is continuously increasing so its $\omega$ is continuously decreasing. So ang swept by $Q$ is less than angle swept by disc. So it will fall in unshaded portion.

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