Question

A body moves along the curved path of a quarter circle.Calculate the ratio of distance to displacement
a) 11:7 b) 7:11 c)11:7√2 d) 7:11√2

Answer 1

Given that the path is a quarter circle, the distance travelled = D = 1/4 x (2x pi (22/7) x R)

 Formula for the circumference of circle being 2 x pi x r

Here the displacement length is the hypotenuse of an isosceles right angle triangle (two sides equal)

  Pythagoras theorem will be applied (a2 +b2 =c2)

Displacement = d = √ [2(R^2)] = √ (2) x R

So ratio = D/d = [1/2 x √ (2)] x pi

Answer 2

Answer:

Given that the path is a quarter circle, the distance travelled = D = 1/4 x (2x pi (22/7) x R)

 Formula for the circumference of circle being 2 x pi x r

Here the displacement length is the hypotenuse of an isosceles right angle triangle (two sides equal)

  Pythagoras theorem will be applied (a2 +b2 =c2)

Displacement = d = √ [2(R^2)] = √ (2) x R

So ratio = D/d = [1/2 x √ (2)] x pi