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?

• A. A
• B. B
• C. C
• D. D

Hint:

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.

Answer 1

The Correct Option is C

Step 1: At the start, the rod touches the circle at point P. Q sits at the far end of the tangent line, a distance equal to the full circumference away.

Step 2: As the tangent point slides around the circle by some arc length, the segment from that point to Q shortens by exactly that same arc length.

Step 3: Repeating this shrinking motion all the way around traces a spiral. It winds once around the circle as the free rod length keeps dropping.

Step 4: When the tangent point completes one full revolution, the free length reaches zero. Q meets the circle exactly at P, giving the tracing in option C.

Answer 2

An easier way in is to track the one quantity that never changes during the whole motion.

1. Option A: The arc already wound plus the rod length still free always adds up to the full circumference. A curve that keeps growing away from the circle would break that fixed total.
2. Option B: The free rod segment always stays tangent to the circle, so its endpoint can never trace a straight line or a hard angle. Any option built from flat segments is ruled out.
3. Option C: The wound arc length plus the free rod length is fixed at the circumference. So the free length must reach zero after one full revolution, and Q must coincide with the circle then, which is what this option shows.
4. Option D: Extra loops around the circle would need more rod length than the circumference provides. A doubled or extended spiral breaks the fixed total length and cannot be correct.

Holding the wound length plus free length fixed at the circumference pins the trace to a single wind that ends on the circle. That matches option C.

the correct answer is Option C.