Question

. An object moves along a circular path of diameter 24 cm with constant speed. If it takes 4 min. to move from a point on the path to the diametrically opposite point. Find (a) The distance covered by the object (b) The speed (c) The displacement (d) average velocity​

Answer 1

Answer:

Distance covered by the object = 37.68 cm

Speed = 9.42 cm/min

Displacement = 24 cm (from A to B)

Velocity = 6 cm/min (from A to B)

Explanation:

Let us assume that the body start from point A so, it moves from a point on the path to the diametrically opposite point, that is B.

Distance covered :

Distance is the total length of path covered by the body.

Here, A to B is the length of the semi circle. So, perimeter of this semi circle will be the distance travelled.

⇒ Distance = Perimeter of semicircle

⇒ Distance = 2πr ÷ 2

⇒ Distance = (2 × 3.14 × 12) ÷ 2

• Radius is 12 because r = diameter/2.

⇒ Distance = (75.36 ÷ 2) cm

⇒ Distance = 37.68 cm

∴ Distance travelled by the object is 37.68 cm.

Speed :

⇒ Speed = $\sf \dfrac{Distance}{Time}$

⇒ Speed = $\sf \dfrac{37.68}{4}$ cm/min

⇒ Speed = 9.42 cm/min

∴ Speed of the object is 9.42 cm/min.

Displacement :

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

Initial position is A and final position is B. The shortest distance is always a straight line. Sp, diameter of the circle is the displacement.

⇒ Displacement = Diameter

⇒ Displacement = 2r

⇒ Displacement = 2(12) cm

⇒ Displacement = 24 cm (from A to B)

∴ Displacement of the body is 24 cm (from A to B).

Velocity :

⇒ Velocity = $\sf \dfrac{Displacement}{Time}$

⇒ Velocity = $\sf \dfrac{24}{4}$ cm/min (from A to B)

⇒ Velocity = 6 cm/min (from A to B)

∴ Velocity of the body is 6 cm/min (from A to B).