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NEET PHYSICSEasy

A mass mm is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:

A

inclined at an angle of 60^{\circ} from vertical.

B

the mass is at the highest point.

C

the wire is horizontal.

D

the mass is at the lowest point.

Step-by-Step Solution

In a vertical circular motion, the tension (TT) in the wire varies depending on the position of the mass mm. According to Newton’s Second Law, the net centripetal force at any point making an angle θ\theta with the downward vertical is Tmgcosθ=mv2RT - mg \cos \theta = \frac{mv^2}{R}, where RR is the radius . This gives the tension as T=mv2R+mgcosθT = \frac{mv^2}{R} + mg \cos \theta . At the lowest point, θ=0\theta = 0^{\circ} (so cosθ=1\cos \theta = 1) and the velocity vv is at its maximum because gravitational potential energy is converted into kinetic energy as the mass descends . Consequently, the tension TT reaches its maximum value at this point, making the wire most likely to break .

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