Question

5. A person travels a distance aR along the circumference of a circle of radius R. The displacement
of the person is -
(a) R
(b) 2R
(c) 2*3.14*R
(d) Zero

​

Answer 1

Correct Question

A person travels a distance πR along the circumference of a circle of radius R. The displacement of the person is -

(a) R

(b) 2R

(c) 2*3.14*R or 2πR [ As π = 3.14 ]

(d) Zero

Solution

Assume that a person starts from point A and the radius of circle is 'R'.

From point A to point B he covers the half of the distance i.e. half of Circumference of circle. If returns back to point A (means starts from point A then B then A again) he covered the one revolution of the circle. Now, the distance covered by the man is equal to the circumference of the circular i.e. 2πr.

But given that the person travels a distance of πR along the circumference of the circle (Means he travels only half of the revolution of circle i.e. semicircle). So, we can say that his initial point is A and final point is B. Now, Displacement is defined as the shortest path travelled by the body or person between the initial point i.e. A and final point i.e. B.

Here, the displacement is equal to diameter or 2*radius and given radius of circle is R. Therefore, the Displacement of the person is 2R.

Option (b) 2R.

Answer 2

GIVEN :-

A person travels a distance πR along the circumference of a circle of radius R.

TO FIND :-

The displacement of the person if it is :-

(a) R

(b) 2R

(c) 2 × 3.14 × R

(d) Zero

SOLUTION :-

We know, the length of the circular path = perimeter of the circular path = 2πR

Given,

The person covers a distance of πR units.

We get :- πR = 2πR/2

Therefore, the person covers a distance half the path.

◙ Now, we know, displacement is the shortest path covered between the initial position and the final position.

So, the movement of the person is from A to B.

Displacement from initial position, A to final position B = AB (Which is the shortest path between A and B)

◙ We observe that, AB is the diameter of the circular path with radius R.

Therefore, the displacement of the person = D = 2R

$\bigstar$ Hence, the answer is (b) 2R.