Question

A body moving in a circle of radius 'r' covers 3/4th of the circle. Find the ratio of the distance to displacement.

Answer 1

the distance= circumference= 3/4 of the circle

circumference of a circle= 2πr

radius(r) = r

for 1 circle= 2πr

for 3/4 circle= 3/4 * 2πr

= 3πr/ 2 units

displacement:

construction- In a circle, taking radius 'r', draw a perpendicular line from the center of the circle, where also the radius meets, and make sure the line is perpendicular to 'r' and touches the circumference. name the point as 'A'. take the starting point of the radius as 'B' and join AB. this forms a right angled triangle

now taking Pythagoras theorem,

AB(hypotenuse) = √r^2 + r^2

= r√2

For the ratio of distance and displacement,

3πr/2 ÷ r√2

= 3πr/2 * 1/r√2

= 3 * 22/7 * 1/2 * 1/√2

= 33/7√2

therefore, the ratio= 33:7√2