Question

A boy is cycling around a circular path of a radius of 70 m. What is the distance and
displacement of the boy when he completes half a revolution?

Answer 1

Explanation:

As per the provided information in the given question, we have:

• A boy is cycling around a circular path of a radius of 70 m.

We are asked to calculate distance travelled and displacement of the boy when he completes half a revolution.

Let us say that the body starts from A. Therefore, after completing half a revolution, it will come to B.

★ Calculating the distance travelled :

Distance is defined as the total path covered by the body. Here, total distance covered will be half pf the circumference of the circular path,

$\\ \twoheadrightarrow \sf { Distance = \dfrac{Circumference}{2} }$

$\\ \twoheadrightarrow \sf { Distance = \dfrac{2\pi r}{2} }$

$\\ \twoheadrightarrow \sf { Distance = \pi r}$

Substituting the values of radius, that is 70 m.

$\\ \twoheadrightarrow \sf { Distance =\Bigg \{ \dfrac{22}{7} \times 70 \Bigg \} \; m}$

$\\ \twoheadrightarrow \sf { Distance =\Bigg \{ 22 \times 10 \Bigg \} \; m}$

$\\ \twoheadrightarrow \bf \underline{ Distance =220\; m}$

Therefore, distance travelled by the body is 220 m.

★ Calculating the displacement :

Displacement is the shortest distance from initial position to final position. Here, initial position is A and final position is B. The shortest distance from A to B is AB, which can be considered as the diameter of the circular path.

$\\ \twoheadrightarrow \sf { Displacement = Diameter}$

$\\ \twoheadrightarrow \sf { Displacement = 2 \times Radius}$

$\\ \twoheadrightarrow \sf { Displacement = (2 \times 70 ) \; m}$

$\\ \twoheadrightarrow \bf\underline { Displacement = 140\; m}$

Therefore, displacement is 140 m.