Question

a mass "m" rotates in a vertical circle of radius R as circular we see at the top in the radius of circle is increased by a factor for circular speed at the top will be ​

Answer 1

Answer:

Explanation:

Considering that we are required to find the relationship between the velocity of the body and that of the radius of the circle, as the circle rotates in a  vertical circle the bottommost point of the circle will have kinetic energy while the topmost point will have potential energy.

As energy can neither be created nor be destroyed according to law of conservation of energy the kinetic energy of the particle at the bottommost point is converted into potential energy at the topmost point,so a minimum amount of kinetic energy must be supplied to the mass to reach the top, which is equal to the potential energy of the mass at the top most point.

Given radius of circle =R

Potential energy at the top most point of the circle= 2×m×g×R.

Let the minimum velocity required by the mass at the bottommost point to reach the top be v.

Applying law of conservation of energy

m×v×v÷2=2×m×g×R

v=2√g×R