JEE Advanced · 2012 · 08 Apr 2012 · Paper 2 · Rotational Mechanics

Consider a disc rotating in the horizontal plane with a constant angular speed

ω

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 has completed

\frac{1}{8}

rotation, (ii) their range is less than half the disc radius, and (iii)

ω

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.
(C)Both $P$ and $Q$ land in the unshaded region.✓ Correct
(D)Both $P$ and $Q$ land in the shaded region.

Answer: (C)

Solution

In the ground frame, both pebbles are projected with the same velocity (disc velocity plus projection velocity relative to disc). During their flight time

t

, the disc rotates through angle

ω t < π /4

. At

t = \frac{π}{4 ω}

, point

P

has moved to

x = ω R \cdot \frac{π}{4 ω} = \frac{π R}{4} > R cos 45° = \frac{R}{2}

. Since the pebbles land before this time and their range is less than

R /2

, both land in the unshaded region. The official answer accepts both (C) and (D), but the working supports (C).

JEE Advanced · 2012 · 08 Apr 2012 · Paper 2 · Single correct option

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JEE Advanced · 2012 · 08 Apr 2012 · Paper 2 · Rotational Mechanics

Solution

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