Question

A particle is moving in a circular path of radius r. The displacement after 3/4 of a circle would be: 1 point (a) Zero (b) ( pi )r (c) (Root 2) r (d) 2( pi ) r

Answer 1

A particle moves in a circle of radius r.

To find:

Displacement of particle after covering ¾ th of circular path

Concept:

Displacement is defined as the minimum/shortest path length between the starting and stopping point of a trajectory (journey)

Calculation:

Look at the diagram to understand better :

Displacement will be :

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

$= > d = \sqrt{2 {r}^{2} }$

$= > d = r \sqrt{2}$

So final answer is :

C) Displacement = r√2

Answer 2

Correct Answer :-

C) r√2

The displacement is r√2 after 3/4 round.

Explanation :-

Given :-

Radius of circular path = r

To Find :-

Displacement after completing 3/4 round of circular path.

Solution :-

We know that,

d = √r² + r²

⇒ d = √2r²

⇒ d = r√2

Hence, the displacement after 3/4 round is r√2.

Important terms :-

Displacement - Displacement is the distance in the particular direction. It is a vector quantity.

It must be kept in mind that distance traveled is always positive. On the other hand displacement may be positive, negative or zero.