Question:
Shown below is a configuration of a circle and a rigid rod. The length of the rod PQ is equal to the circumference of the green circle. The rod tangentially revolves around the circle till point Q reaches point P. Which option represents the CORRECT tracing of point Q?
Shown below is a configuration of a circle and a rigid rod. The length of the rod PQ is equal to the circumference of the green circle. The rod tangentially revolves around the circle till point Q reaches point P. Which option represents the CORRECT tracing of point Q?
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In problems involving motion along a curve, understand the path traced by a point on the moving object and match it with the correct option.
Updated On: Jul 7, 2026
A
B
C
D
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The Correct Option is C
Approach Solution - 1
Step 1: The rod moves tangentially around the circle. Since the length of the rod is equal to the circumference of the circle, point Q will trace a specific curve as the rod moves.
Step 2: Visualize the motion of point Q and match it with the correct tracing shown in the options.
Step 3: Option (C) shows the correct tracing of point Q as the rod moves around the circle.
Step 2: Visualize the motion of point Q and match it with the correct tracing shown in the options.
Step 3: Option (C) shows the correct tracing of point Q as the rod moves around the circle.
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Approach Solution -2
This question is about the curve a point traces when a taut rod unwinds while staying tangent to a circle. That curve is a classic involute construction.
- Option A: A path that keeps expanding outward without ever tightening back cannot be right. The free length of rod from the tangent point to Q keeps shrinking as the rod winds, so the trace must curve back in.
- Option B: A path with sharp corners or straight jumps does not match this motion. The tangent point moves continuously around the circle, so the trace has to curve smoothly too.
- Option C: A smooth spiral that winds once around the circle and closes onto the circle when the free length hits zero matches this setup exactly. Since the rod length equals the circumference, Q lands back on the circle right at point P after one full wind.
- Option D: A trace that loops more than once, or ends away from the circle, does not fit. The rod only has enough length for a single revolution before the free segment runs out.
The free rod length keeps falling from the full circumference down to zero as the rod winds. Only option C shows a curve that behaves this way and lands exactly on P.
the correct answer is Option C.
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