A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is (a) the same throughout the motion. (b) minimum at the highest position of the circular path. (c) minimum at the lowest position of the circular path. (d) minimum when the rope is in the horizontal position.

Answer: (b). At angle θ from the top: T + mgcos θ = mv²/r With constant v, T = mv²/r - mgcos θ is least when cos θ = 1 (top) So the answer is (b) minimum at the highest position.

A stone of mass m, tied to a string is being whirled in a vertical… | JEE Main 2022 (24 Jun, Shift 2)

Q13JEE Main 2022 · 24 JUN · SHIFT 2Easy

Vertical Circle: Speed & Tension

A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

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Answer: (b)

At angle $\theta$ from the top: $T + mg\cos\theta = \frac{mv^2}{r}$
With constant $v$ , $T = \frac{mv^2}{r} - mg\cos\theta$ is least when $\cos\theta = 1$ (top)
So the answer is (b) minimum at the highest position.

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