Question

a body is describing circular path when it completes one and half of a circle the ratio of distance travelled to its displacement is ​

Answer 1

Given:

• Body covered 1½ trajectory in a circle.

To find:

Ratio of distance to displacement ?

Calculation:

Distance is the total path length & Displacement is the shortest length between the starting and stopping point.

• Let radius of circle be r :

Distance will be :

$d = 2\pi r + \pi r = 3\pi r$

Displacement will be :

• It is calculated using Pythagoras' Theorem.

$l = \sqrt{ {r}^{2} + {r}^{2} } = r \sqrt{2}$

So, the required ratio is :

$d : l = 3\pi r : r \sqrt{2}$

$\implies d : l = 3\pi : \sqrt{2}$

So, the ratio is 3π : √2.

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Answer 2

Step 1: Given data

Distance travelled $=d$

Displacement $=D$

$\frac{d}{D} =?$

Step 2: Calculating the required ratio

If the body traverses along a circle and completes one and half of a circle, then total distance travelled by the body is calculated as,

$2\pi r+\pi r=3\pi r$

Since, displacement is the shortest path between the initial position and final position of the body,

thus, it can be calculated using pythagoras' theorem,

Let $r$ be the radius of the circle.

$\therefore D^{2} =r^{2} +r^{2} =2r^{2}$

$D=\sqrt{2} r$

Therefore,

$\frac{d}{D} =\frac{3\pi r}{\sqrt{2}r } =\frac{3\pi }{\sqrt{2} }$

Hence, the required ratio is $3\pi :\sqrt{2}$.

#SPJ2