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 135°=-0.7)

Solution

Physics sir · 4 steps

Use the arc length to get the radius, then the cosine rule on triangle OAB gives the straight line AB.

1. Radius from arc. The distance travelled is the arc AB, which subtends 135° = 3π/4 rad at the centre. So 60 = r × 3π/4, giving r = 80/π ≈ 25.46 m.
2. Displacement is chord. Displacement is the straight line from A to B. In triangle OAB, OA = OB = r and the angle between them is 135°, so apply the cosine rule.

   AB = √(r² + r² - 2r²cos 135°) = r√2(1 - (-0.7)) = r√3.4

3. Put in numbers. √3.4 ≈ 1.844, so AB ≈ 25.46 × 1.844 ≈ 46.96 m.
4. So. The magnitude of displacement is about 47 m, option (b).

The idea to keep. On a circle, distance is the arc rθ (with θ in radians) and displacement is the chord. The cosine rule gives the chord, and the chord is always shorter than the arc.

Answer from the NTA final answer key. Solution by PrepWiser.