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A stone of mass m tied to the end of a string revolves in a vertical circle of radius R. The net forces at the lowest and highest points of the circle directed vertically downwards are : [Choose the correct alternative] Lowest Point Highest Point (a) mg – T₁ mg + T₂ (b) mg + T₁ mg – T₂ (c) mg + T₁ – (m v ²₁ ) / R mg – T₂ + (m v ²₁ ) / R (d) mg – T₁ – (m v ²₁ ) / R mg + T₂ + (m v ²₁ ) / R T₁ and v₁ denote the tension and speed at the lowest point. T₂ and v₂ denote corresponding values at the highest point.

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Solution

The free body diagram of the stone at the lowest point is shown in the figure below.



According to Newton’s second law of motion, the net force acting on the stone at this point is equal to the centripetal force,

F net = m v 1 2 R T 1 mg= m v 1 2 R

Where, T 1 is the tension in the string, v 1 is the velocity of the stone and g is the acceleration due to gravity at the lowest point.

The free body diagram of the stone at the highest point is shown in the figure below.



According to Newton’s second law of motion, the net force acting on the stone at this point is equal to the centripetal force,

F net = m v 2 2 R T 2 +mg= m v 2 2 R

Where, T 2 is the tension in the string and v 2 is the velocity of the stone at the highest point.

Hence, option (A) is correct.


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