Question

If a body moves in a circular path of radius 'a' what are distance and displacement in:
i)2rounds
ii)2 1/2rounds.
can someone pls ans this with steps pls I beg​

Answer 1

Required Answer :

Here, we are given that the radius of a circular path is 'a' on which a body travels. We have to find its distance and displacement in 2 rounds and 2 and half rounds.

⑴

In the first part of the question, we have to find the distance and displacement in 2 rounds.

Since it moves on circular path, so distance covered in 1 round is the circumference of the circular path. As we know that,

$\longmapsto$ Circumference = 2πr

• Radius = a [Given]

$\longmapsto$ Circumference = 2πa

So, distance covered by the body in one round is 2πa. Hence,

$\longmapsto$ Distance covered in two rounds = 2 × 2πa

$\longmapsto$ Distance covered in two rounds = 4πa

$\dashrightarrow \boxed { \sf { Distance = 4 \pi a}}$

Therefore, distance covered by the body in two rounds is 4πa.

Body comes to its initial position again after travelling a certain distance. So, its initial and final position is same. Therefore, its displacement is 0 .

$\dashrightarrow \boxed { \sf { Displacement = 0}}$

⑵

In the second part of the question, we have to find the distance and displacement of the body in 2 and half rounds.

• Distance covered by it in 2 rounds is 4πa.

$\longmapsto$ Distance covered in half round = ½ × Distance covered in one round

$\longmapsto$ Distance covered in half round = ½ × 2πa

$\longmapsto$ Distance covered in half round = πa

So,

$\longmapsto$ Distance covered in 2½ rounds = Distance covered in 2 rounds + Distance covered in half round

$\longmapsto$ Distance covered in 2½ rounds = 4πa + πa

$\longmapsto$ Distance covered in 2½ rounds = 5πa

$\dashrightarrow \boxed { \sf { Distance = 5 \pi a}}$

Therefore, distance covered by the body in 2½ rounds is 5πa.

__

Here, let's say the body starts to move from point A and then it covers 2 rounds. After two rounds it's displacement is 0. Then it covers half round and comes to point B. So, its displacement is AB.

AB is the diameter of the circle. We know that,

• Diameter of circle = 2 × Radius

→ Displacement = 2 × a

$\dashrightarrow \boxed { \sf { Displacement = 2a}}$

Therefore, displacement of the body is 2a.