Question

19. A particle moves along a circular path of radius 'r' and completes
3/4 part of the circle. Calculate
(i) Distance travelled by the particle
(ii) the displacement of the particle​

Answer 1

Given:

Particle moves along the circular path of radius r and completes ¾ th part of circle.

To find:

• Distance

• Displacement of particle

Concept:

• Distance is defined as the the total path length travelled by an object . Its a scalar quantity having only magnitude and direction

• Displacement is defined as the shortest length between starting and stopping point. Its a vector.

Calculation:

$distance = \dfrac{3}{4} \bigg \{2\pi r \bigg \}$

$= > distance = \dfrac{3\pi r}{2}$

Now , Displacement :

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

$displacement = \sqrt{ 2{r}^{2} }$

$displacement = r \sqrt{2}$

Answer 2

Given that:

• A particle moves along a circular path of radius 'r' and completes

To Find :

• Distance travelled by the particle.

• Displacement of the particle.

Concept Used:

• Distance is the length of actual path travelled.

• Displacement is the length of shortest possible path between two points.

Solution:

Since, the particle has completed 3/4th part of the circular path of radius r.

So, Distance = 3/4*(2πr)

Distance = 3(πr)/2 units.

Displacement = √(r^2+r^2)

Displacement = r√2 units.

[Refer to the attachment for diagram]

Hope this helps