Question

A body covers a distance of 5 m along a semicircular path from its one end to another end. Then
the ratio of its distance covered to its displacement is :
(A) 11:7
(B) 12:5
(C) 8:3
(D) 7:5​

Answer 1

From given diagram,

• Diameter (d) = 5m
• AB = 2(radius) = 2r
• Initial point of body= A
• Final point of body= B.

To Find,

• Ratio of distance and displacement.

Here,

Distance = Circumference of semi circle

And Circumference of circle = πr.

Then,

$\tt \implies \: Distance = \pi \: r \\ \tt \implies \: 5 = \pi \: r \\ \tt \implies \: r = \frac{5}{\pi}$

Now,

$\tt Displacement = distance \: \\ \tt between \: A \: and \: B \\ \tt \implies \: displacement = 2r \\ \tt \implies \: displacement = 2 \times \frac{5}{\pi} \\ \tt \implies displacement = \frac{10}{\pi} \\ \tt \implies displacement = \frac{70}{22} \\ \tt \implies displacement = \frac{35}{11}$

Now we have,

Distance = 5

and Displacement = 35/11.

$\\ \\ \\ \tt \implies Ratio = \frac{Distance}{Displacement} \\ \: \tt \implies ratio = \frac{5}{ \frac{35}{11} } \\ \tt \implies ratio = \frac{55}{35} \\ \tt \implies ratio = \frac{11}{7}$

$\\ \\ \large \implies \boxed {\boxed {\tt \blue {Option-A \: is \: correct }}}$

Answer 2

Answer:

Explanation:

The body travelled 5 metres along the semicircular path.

This distance is equal to one-half of the circle's circumference, of which this semicircle is a part.

If a semicircular path has a radius of "r," then "l = pi r" or "r = l/pi" applies.

Dimensions of displacement are given by diameter = 2r = (2l)/(pi):. Distance/displacement are equal to (l)/(2l/pi) = (pi)/(2)'.

So the answer is option A) 11:7

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