For a particle rotating in a vertical circle with uniform...

For a particle rotating in a vertical circle with uniform speed, the maximum and minimum tension in the string are in the ratio $5: 3$. If the radius of vertical circle is $2 \mathrm{~m}$, the speed of revolving body is $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$ (A) $\sqrt{5} \mathrm{~m} / \mathrm{s}$ (B) $4 \sqrt{5} \mathrm{~m} / \mathrm{s}$ (C) $5 \mathrm{~m} / \mathrm{s}$ (D) $10 \mathrm{~m} / \mathrm{s}$

For a particle rotating in a vertical circle with uniform speed, the maximum and minimum tension in the string are in the ratio $5: 3$. If the radius of vertical circle is $2 \mathrm{~m}$, the speed of revolving body is $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(A) $\sqrt{5} \mathrm{~m} / \mathrm{s}$
(B) $4 \sqrt{5} \mathrm{~m} / \mathrm{s}$
(C) $5 \mathrm{~m} / \mathrm{s}$
(D) $10 \mathrm{~m} / \mathrm{s}$

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Key Concepts

Gravitational Force Effects on Tension

In vertical circular motion, gravitational force plays a crucial role by affecting the net tension in the string. Its direction relative to the centripetal requirement changes as the body moves, leading to a variation in tension; at the bottom of the circle, gravity adds to the tension required to provide centripetal force, while at the top, it opposes it.

Tension in a String Under Circular Motion

Tension in the string is the force that acts along the string to provide the necessary centripetal force. Its magnitude changes with the position of the particle in a vertical circle, due to the influence of gravity, and can be determined using Newton’s second law by balancing the forces acting on the particle.

Uniform Circular Motion

This concept involves a body moving in a circular path at a constant speed. Although the speed is constant, the continuous change in direction results in an acceleration towards the center of the circle, which is characterized as centripetal acceleration.

Centripetal Force

Centripetal force is the net force required to keep an object moving in a circular path. It is calculated using the formula v²/R, where v is the speed of the object and R is the radius of the circle. In circular motion problems, this force is what maintains the trajectory of the moving body.

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