JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Kinematics

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A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be : (Given

cos 13 5^{\circ} = - 0.7

)

(A)42 m
(B)47 m✓ Correct
(C)19 m
(D)40 m

Answer: (B)

Solution

The arc length is

d = R θ

, where

θ = 3 π /4

radians. From

60 = R (3 π /4)

, we get

R = 80/ π

m.

The displacement is the straight-line distance from A to B. Using the cosine rule for the triangle formed by the two radii and the chord:

Displacement = R^{2} + R^{2} - 2 R^{2} cos 13 5^{\circ} = 2 R^{2} (1 - cos 13 5^{\circ})

= 2 R^{2} (1 + 0.7) = 3.4 R^{2} = R 3.4

= \frac{80}{π} 3.4 \approx \frac{80}{3.14} \times 1.84 \approx 47 m

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Single correct option

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