Question

A body moves along a circular track of radius (r ). It starts from one end of a diameter, moves along the circular track and completes one and a half revolutions. The ration of distance traveled by the body to its displacement is. (question no 5, 6)

Answer 1

Answer:

Given:

Radius of circular track = r

Body starts from one end of diameter , completes 1½ revolutions .

To find:

Ratio of distance to displacement

Concept:

Distance is the total path length travelled by the body in a specified time period

Whereas , Displacement is the shortest length between starting point and stopping point in a trajectory.

Calculation:

Distance be d

$d = path \: length$

$= > d = 2\pi r + \pi r$

$= > d = 3\pi r$

Let displacement be s . Since the body started from one end of diameter and made 1½ turns it means it ended at other end of the diameter.

So Displacement will be equal to the diameter.

$s = diameter$

$= > s = 2 \times (radius)$

$= > s = 2r$

So final answer :

Ratio will be 3πr : 2r

=> 3π : 2

$\boxed{\red{\huge{\bold{3\pi \: : 2 }}}}$

Answer 2

GiveN :

• A body moves along a circular track of radius r.
• It starts from one end of Diameter and Travels 1 and half revolution.

To FinD :

• Relationship between Distance and Displacement

SolutioN :

$\bigstar {\underline{\sf{According \: To \: The \: Question}}}$

As we know that,

The body completes 1 and half revolution. So, It means

⇒Distance = Circumference of circle + Circumference of semi circle

⇒Distance = 2πr + πr

⇒Distance = 3πr

∴ Distance Travelled by body is 3πr

__________________________

Also, we know that :

Body travels from A to B.

So,

⇒ Displacement = Diameter

⇒Displacement = 2*r

⇒Displacement = 2r

∴ Displacement of body is 2r

_______________________

Relationship between Distance and displacement

⇒Ratio = 3πr/2r

⇒Ratio = 3π/2

∴ Ratio is 3π:2