Vertical circular motion is an example of non-uniform motion...

Vertical circular motion is an example of non-uniform motion and for completion of vertical circular motion the maximum velocity at the start of vertical motion from lowest point is
(A) $\sqrt{g R}$
(B) $\geq \sqrt{5 g R}$
$(\mathrm{C})=\sqrt{5 g R}$
(D) $\leq \sqrt{5 g R}$

Key Concepts

Centripetal Force

Centripetal force is the net force directed towards the center of a circular path that keeps an object moving in that circle. For vertical circular motion, this force must be sufficient at all points of the path, especially at the top of the circle, to overcome gravitational pull and maintain the object's trajectory, ensuring that it does not fall out of its circular path.

Conservation of Energy

The conservation of energy principle plays a crucial role in analyzing vertical circular motion, where the kinetic energy at one point is converted into gravitational potential energy at another. By applying energy conservation, one can determine the required initial speed at the lowest point of the circle to ensure that the object has enough energy to complete the loop.

Vertical Circular Motion

This concept refers to any motion where an object travels along a circular path that lies in a vertical plane. In such motions, gravity plays a significant role by affecting the speed and the forces acting on the object, unlike horizontal circular motion where gravity is usually balanced by normal forces.

Non-uniform Motion

In vertical circular motion, the speed of the moving object is not constant because gravitational force causes the acceleration to vary at different points along the path. This variation makes the motion non-uniform, meaning that kinetic energy is continuously converted into potential energy and vice versa as the object moves along the circle.

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