As shown in the figure, a particle is moving with constant speed π m/s. Considering its motion from A to B, the magnitude of the average velocity is: (a) π m/s (b) 1.5√(3) m/s (c) √(3) m/s (d) 2√(3) m/s

Answer: (b). Displacement AB = chord for 120°: 2rsin 60° = r√3. Arc AB = (2π r)/(3), so time t = (2π r/3)/(π) = 2r/3 s. vavg = (r√3)/(2r/3) = 1.5√3 m/s. So the answer is (b) 1.5√(3) m/s.

As shown in the figure, a particle is moving with constant speed π… | JEE Main 2023 (6 Apr, Shift 2)

Q26JEE Main 2023 · 6 APR · SHIFT 2Medium

Angular Variables

As shown in the figure, a particle is moving with constant speed $\pi\text{ m/s}$ . Considering its motion from $A$ to $B$ , the magnitude of the average velocity is:

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Answer: (b)

Displacement $AB$ = chord for $120^\circ$ : $2r\sin 60^\circ = r\sqrt3$ .
Arc $AB = \frac{2\pi r}{3}$ , so time $t = \frac{2\pi r/3}{\pi} = \frac{2r}{3}$ s.
$v_{avg} = \frac{r\sqrt3}{2r/3} = 1.5\sqrt3$ m/s.
So the answer is (b) $1.5\sqrt{3}$ m/s.

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