A stone of mass 200 g attached to a string is made to revolve in a horizontal circle of radius 1.5 m at a…

Analyze the question: A 200 g stone moves in a circle of radius 1.5 m at 5 m/s. The question says "horizontal circle" but also asks for tension "at the bottom of the circle", which suggests a vertical circle. I'll work through both readings.

Concept: The net force toward the centre provides the centripetal force, F = mv²/r.

Data:

• m = 0.2 kg
• v = 5 m/s
• r = 1.5 m
• g = 10 m/s²

Centripetal force: F = mv²/r = (0.2 × 25)/1.5 = 5/1.5 ≈ 3.33 N

Reading 1: truly horizontal circle Tension alone supplies the centripetal force, so T ≈ 3.3 N (option B). This would be the same at every point on the circle. Strictly, a string can't stay perfectly horizontal while carrying the weight, so this reading is idealised.

Reading 2: vertical circle, at the bottom At the bottom, tension acts upward (toward the centre) and weight acts downward:

T − mg = mv²/r T = mv²/r + mg = 3.33 + (0.2 × 10) = 3.33 + 2.0 = 5.33 N ≈ 5.3 N

This matches option A.

Which one is right? The phrase "at the bottom of the circle" only makes sense if the weight matters, so the vertical-circle calculation is intended. That gives 5. The word "horizontal" in the question looks like a wording slip. If the circle really were horizontal, the answer would be 3.3 N, but then "at the bottom" would have no meaning.

Answer: T = 5.3 N, option A.

Exam tip: For vertical circles, remember:

• Bottom: T = mv²/r + mg (tension is largest here)
• Top: T = mv²/r − mg (tension is smallest here)

Check the position named in the question before choosing the formula.