Question

An insect is crawling on a cycle rim of radius r. What will be the distance and displacement

of the insect in half revolution (ii) in one complete revolution?​

Answer 1

Answer:

i) Distance = 1/2 × 2pi r ( as circumference of circle is 2pi r ; for half circle it will be 1/2 × 2pi r )

Displacement: r + r = 2r ( its the distance between initial n final positions, so for half revolution the displacement ll be the diameter i.e. 2r)

ii) Distance = 2pi r ( as circumference of circle is 2pi r)

Displacement: 0 ( as the initial n final positions are same, displacement will be 0 for complete revolution)

Answer 2

Given: An insect is crawling on a cycle rim of radius r.

To find: The distance and displacement of the insect in half revolution and in one complete revolution.

Solution:

• When an insect is crawling on a cycle rim, it is in a state of circular motion.

• Distance is the measure of the path traversed by the body in a certain time whereas, displacement is the shortest distance travelled by the body between the final and initial position in a certain time.

(i)

• When the insect has completed half the revolution, the distance covered by it is half of the circumference of the cycle rim.
• Circumference is given by the formula,

        $C = 2\pi r$

• Here, C is the circumference and r is the radius of the cycle rim.

• Since the distance is half of circumference,

        $distance = \frac{2\pi r}{2}$

                      $=\pi r$

• The displacement would be the diameter (twice the radius), as it is the shortest distance travelled.

        $displacement = 2r$

(ii)

• In case of one complete revolution, the distance become the entire circumference, that is, 2πr.
• The displacement would be zero since the initial and the final positions are the same.

Therefore, the distance and displacement of the insect in half revolution is πr and 2r respectively. The distance and displacement of the insect in one complete revolution 2​πr and zero respectively.