Question

A body moves along a curved path of a quarter circle. what is the ratio of distance to displacement?

Answer 1

Distance = πr/2

Displacement = r√2

Distance/ Displacement = πr / (2r√2) = π/(2√2) = (π√2) / 4

Ratio of distance to displacement is π : 2√2 (or) π√2 : 4

Answer 2

Given :Body moves in quarter part of circle.So, distance will be quarter of circumference of circle=2πr/4=πr/2Displacement will be shortest distance .From the figure : AB is the Displacement .It forms a right angle traingle.AB² =displacement=Hypotenuse=√(r²+r²)
=√2r²=r√2

Ratio of distance to displacement =πr/2xr√2
=π/2√2
=π/2√2
=22/√2x(2x7)
=11/√2x7

∴ Ratio of Distance to displacement is 11 : √2(7)