Question

A boy moves on a circular distance of radius R. Starting from a point A he moves to a point B and radius at these two point subtend an angle of 1200at Centre. The ratio of the distance travelled to the displacement made by him is (a) ∏/(3√3) (b) 2∏/(√3) (c) 2∏/(3√3) (d) 4∏/(3√3)​

Answer 1

Answer:

As per the provided information in the given question, we've :

A boy moves on a circular distance of radius R. Starting from a point A he moves to a point B which is on the other end of the diameter AB.

We are asked to calculate the ratio of the distance travelled to the displacement made by him. In order to calculate the ratio, we need to calculate the distance travelled and the displacement.

Distance travelled :

Since, the boy covers the distance on a circular path. Thus, we need to apply the formula of perimeter of the circle, but since it starts from A and moves to a point B which is on the other end of the diameter AB, so distance travelled will be the half of the perimeter.

⇒ Distance travelled = Perimeter of circular path ÷ 2

⇒ Distance travelled = (2πr) ÷ 2

r = R(Radius)

⇒ Distance travelled = (2πR) ÷ 2

⇒ Distance travelled = 2πR

∴ Distance travelled is 2πR.

Displacement :

Displacement is the shortest distance from the initial position to the final position.

Here,

Initial position = Point A

Final position = Point B

Shortest distance between two points is always a straight line. So, shortest distance from point A to point B is AB. AB is also the diameter of the circle.

⇒ Displacement = AB

⇒ Displacement = Diameter of circular path

⇒ Displacement = 2 × r

r = R(Radius)

⇒ Displacement = 2R

∴ Displacement is 2R.

Now, finding the ratio :

\longrightarrow \sf {Ratio = \dfrac{Distance}{Displacement} }⟶Ratio=

Displacement

Distance

\longrightarrow \sf {Ratio = \dfrac{2\pi R}{2R} }⟶Ratio=

2R

2πR

\longrightarrow \sf {Ratio = \dfrac{\pi }{1} }⟶Ratio=

1

π

\longrightarrow \sf { Ratio = \pi \ratio 1}⟶Ratio=π:1

∴ The ratio of the distance travelled to the displacement made by him is π : 1.

Option (B) is correct.

Explanation:

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