Question

A particle is moving along a circular track of radius 1 m with a uniform speed. The ratio of the distance covered and the displacement in half revolution is:

• A. 1 : 1
• B. \( \pi : 1 \)
• C. 2 : \( \pi \)
• D. \( \pi : 2 \)

Hint:

In circular motion, the distance covered in half revolution is \( \pi \times r \) and the displacement is the diameter \( 2r \).

Answer 1

The Correct Option is B

In a circular motion, the distance covered in half revolution is the length of the semicircle: \[ \text{Distance covered} = \pi \times \text{radius} = \pi \times 1 = \pi \, \text{m} \] The displacement is the straight line joining the initial and final points, which is the diameter of the circle: \[ \text{Displacement} = 2 \times \text{radius} = 2 \times 1 = 2 \, \text{m} \] Therefore, the ratio of distance covered to displacement is: \[ \frac{\pi}{2} = \pi : 1 \] Thus, the correct answer is \( \pi : 1 \).