Question

An object is moving along the circumference of a circular track of radius 'R'. What is the displacement of the object when it covers 3/4 th of its circumference?
(Please explain in detail with steps) ​

Answer 1

Solution :

Given :-

An object is moving along the circumference of a circular path track of radius 'R'.

To Find :-

Displacement of the object when it covers 3/4th of its circumference.

Please see the attached image for better understanding.

Concept :-

Displacement is defined as the shortest distance between initial abd final position of moving object.

Displacement is a vector quantity.

Calculation :-

$\implies\bf\:displacement(D)=\sqrt{R^2+R^2}\\ \\ \implies\sf\:D=\sqrt{2R^2}\\ \\ \implies\underline{\boxed{\bf{\purple{D=\sqrt{2}R}}}}$

Answer 2

Refer to the figure in the attachment .

Answer :

Let the radius of the circle with centre O be R.

We know, that displacement of a body is the shortest distance covered by it. It had direction and magnitude, hence it is a vector quantity. Also, displacement of a body can't be zero.

When the body covers 3/4th of the circumference of the circle, then the two radius forms a right angled triangle AOB.

Now, by using Pythagoras theorem

Perpendicular²+Base²=Hypotenuse²

And, here the displacement of the body is the hypotenuse of the triangle as the body moves from initial to final position.

$So, displacement = \: \sqrt{ {r}^{2} + {r}^{2} } \\ \: \: \: \: \: \: \: displacement = \sqrt{2 {r}^{2} }$

Therefore, displacement of the body when it covers 3/4th of the circumference is $\sqrt{2 {r}^{2} }$.