JEE Main 2025 Apr 2 Shift 2, Physics Q15: Motion In Two And Three Dimension

JEE Main2025Apr 2, Shift 2Physics

A sportsman runs around a circular track of radius $r$ such that he traverses the path $A B A B$ . The distance travelled and displacement, respectively, are

A
$2 r, 3 π r$
B
$3 π r, π r$
C
$π r, 3 r$
D
$3 π r, 2 r$

Solution

$A$ and $B$ are diametrically opposite, separated by a straight-line distance of $2 r$ and by an arc length of $π r$ along the circle.

The sportsman covers three semicircles in sequence ( $A \to B \to A \to B$ ):

Total distance $= 3 \times π r = 3 π r$ .

Final position is $B$ while the start was $A$ , so the net displacement is the straight chord $A B = 2 r$ .

$∴$ distance $= 3 π r$ , displacement $= 2 r$ .

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JEE Main 2025 Apr 2 Shift 2, Physics Q15: Motion In Two And Three Dimension

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