JEE Physics 2025 Question with Solution

Given: A sportsman moves on a circular track of radius $r$ along the path $A \to B \to A \to B$.

Find: The distance travelled and displacement, respectively.

Distance is the total path length covered, while displacement is the straight-line distance from the initial point to the final point.

Points $A$ and $B$ are opposite ends of a diameter, so each motion from $A$ to $B$ or $B$ to $A$ is one semicircle.

Distance of one semicircle:

$$\pi r$$

Total distance for three semicircular arcs:

$$3 \times \pi r = 3\pi r$$

The initial point is $A$ and the final point is $B$, so the displacement is the straight-line distance between $A$ and $B$, which is the diameter:

$$2r$$

Therefore, the distance travelled is $3\pi r$ and the displacement is $2r$. The correct option is D.

Given: The sportsman follows the sequence $A \to B \to A \to B$ on a circular track of radius $r$.

Find: Distance travelled and displacement.

Step 1: From $A$ to $B$, the sportsman covers one semicircular arc.

$$\text{Arc length} = \pi r$$

Step 2: From $B$ to $A$, he again covers one semicircular arc.

$$\text{Arc length} = \pi r$$

Step 3: From $A$ to $B$, he covers one more semicircular arc.

$$\text{Arc length} = \pi r$$

So total distance is:

$$\pi r + \pi r + \pi r = 3\pi r$$

Step 4: Initial position is $A$ and final position is $B$. The displacement is the straight-line distance between these two points.

Since $A$ and $B$ are endpoints of a diameter:

$$\text{Displacement} = 2r$$

Hence, the required pair is $3\pi r, 2r$.