Question

A body covered a distance of 5 m along a semicircular path. The ratio of distance to displacement
is
(A) 11:7
(C) 5:12
(B) 12:5
(D) 7:11​

Answer 1

It travels semicircular path

Distance = πr

5 = πr

r = 5/π

Displacement = Distance between initial position and final position

= 2r

= 2 * 5/π

= 10/π metres

Ratio of distance to displacement

= 5 / (10 / π)

= π/2

= 11/7

= 11 : 7

Answer 2

Answer:

The ratio of distance to displacement is 11 : 7 .

Explanation:

• Distance is measure of total path travelled by a body between any two points A and B.
• Displacement is the shortest distance between any two points A and B.
• Distance is a scalar quantity while displacement is a vector quantity.

Given that :

• A body covered a distance of 5 m along a semicircular path.

Solution :

• Distance covered by body is equal to circumference of semi circle i.e. πr .
• Displacement of body is equal to the diameter of the circle i.e. 2r .
• Considering, a semi circle of radius, r. Then, distance covered by body is πr which is equal to 5 m . (given)

$\pi r = 5 \\ r = \frac{5}{\pi} \: \: \: \: \: \: \: \: \: \: - - - (1)$

• Now, displacement of the body is equal to

$displacememt = 2r \\ = 2 \times \frac{5}{\pi} \\ = \frac{10}{\pi} \\ using \: \pi = \frac{22}{7} \\ displacement = \frac{10 \times 7}{22} = \frac{35}{11} \: \: \: - - - (2)$

• The ratio of distance to displacement is given by:

$\frac{distance}{displacement} = \frac{5}{ \frac{35}{11} } = \frac{5 \times 11}{35} \\ = \frac{11}{7}$

• Hence, the ratio of distance to displacement is 11 : 7 .