Question

A particle moves on a
circular path of radius
r. If completes one revolution in 40s .calculatedistance and displacement in 12min 20s
​

Answer 1

GiveN :-

A particle moves on a  circular path of radius  r. It completes one revolution in 40 s.

• Length of the path = 2πr

• Time taken to complete one revolution around the path = 40 s

TO DeterminE :-

The distance and displacement in 12 min 20 s.

AcknowledgemenT :-

Distance is the total length of the path covered from the initial position to the final position.

Displacement is the change in position vector, i.e. shortest length of the path between the initial position and the final position.

AnsweR :-

Time = 12 mins 20 s

⇒Time = (12 × 60) + 20 s

⇒Time = 740 s

Number of revolutions in 740 s :-

1 revolution takes 40 s

In 740 s, no. of revolutions = 740/40 = 74/4 = 18.5 revolutions.

So, the particle takes 18 full revolutions along-with a half revolution.

$\rule{200}{2}$

• Displacement = displacement of 18 full revolutions + displacement of a half revolution

After 18 full revolutions, the initial position is same as the final position.

⇒ Displacement = 0 + displacement of a half revolution

⇒Displacement = diameter of the circular field

⇒Displacement = 2r

$\rule{200}{2}$

• Distance covered = distance of 18 full revolutions + distance of a half revolution

⇒ Distance covered = 18 × 2πr + 2πr/2

⇒ Distance covered = 36πr + πr

⇒ Distance covered = 37πr

$\rule{200}{2}$

Answer 2

Given

A particle moves in a circular path of radius r.

Time taken to complete one revolution = 40 seconds

To find

Distance and displacement in 12 mins and 20 seconds = ?

Now,

Time = 12 mins + 20 secs

        = 720 + 20

        = 740 secs

If one revolution takes 40 seconds, then the number of revolutions taken in 740 seconds will be:

$= \sf \dfrac{740}{40}$

$= \sf 18.5 \ revolutions$

Displacement = Diameter of the circular field ( Since, its is 18 revolutions and a half revolution)

$\boxed{\boxed{\bold{Therefore, \ displacement \ is \ 2r}}}}}}}}}}$

Distance

= $\sf 18*2\pi r + \dfrac{2\pi r }{2}$

$= 36\pi r + \pi r$

$= 37 \pi r$

$\boxed{\boxed{\bold{Therefore, \ distance \ is \ 37\pi r}}}}}}}}}}$