Which of the following statement is true if a body moves in a semicircular track whose radius is R

The correct option is Both (a) and (b) are correct.

Let us analyze the motion of the body along a semicircular track of radius $R$ to understand why both statements (a) and (b) are true.

1. Distance Travelled (Statement b):
Distance is defined as the actual path length covered by a moving object.
A full circular path of radius $R$ has a circumference given by:
$C=2\pi R$
Since the track is semicircular (which is exactly half of a full circle), the distance travelled by the body is half of the circumference:
$\text{Distance}=\frac{2\pi R}{2}=\pi R$
Therefore, the distance travelled by the body is $\pi R$. This makes statement (b) correct.

2. Displacement of the Body (Statement a):
Displacement is the shortest straight-line distance between the initial position and the final position of the body.
For a semicircular path, the initial and final positions are at the two opposite ends of the diameter of the circle.
The straight-line distance between these two opposite ends is equal to the diameter of the circular track:
$\text{Displacement}=\text{Diameter}=2R$
Therefore, the displacement of the body is $2R$. This makes statement (a) correct.

Since both statement (a) and statement (b) are correct, the correct choice is Both (a) and (b) are correct.