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

(D) $1.5 \sqrt{3} \mathrm{~m} / \mathrm{s}$

(A) $\pi \mathrm{m} / \mathrm{s}$

(B) $\sqrt{3} \mathrm{~m} / \mathrm{s}$

(C) $2 \sqrt{3} \mathrm{~m} / \mathrm{s}$

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Kinematics

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) $3 m / s$
(C) $23 m / s$
(D) $1.5 3 m / s$ ✓ Correct

Answer: (D)

Solution

Let the orbit radius be

R

. The particle travels the

12 0^{\circ}

arc from A to B, of length

\frac{2 π R}{3}

, at constant speed

π

m s

^{- 1}

, so the time taken is

Δ t = \frac{2 π R /3}{π} = \frac{2 R}{3}

. The displacement is the chord joining A and B, of length

2 R sin 6 0^{\circ} = R 3

. The magnitude of the average velocity is

\frac{R 3}{2 R /3} = \frac{3 3}{2}

, that is

1.5 3

m s

^{- 1}

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Single correct option

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