Question

A body of mass ·m' is moving along a circle of radius 'r' with linear speed 'v'. Now, to change the linear speed to `V/2` and to move it along the circle of radius '4r', required change in the centripetal force of the body is ______.

Options

• decrease by `15/16`

• decrease by `5/16`

• increase by `9/16`

• increase by `11/16`

Answer 1

A body of mass ·m' is moving along a circle of radius 'r' with linear speed 'v'. Now, to change the linear speed to `V/2` and to move it along the circle of radius '4r', required change in the centripetal force of the body is decrease by `15/16`.

Explanation:

`F_1=(mv^2)/r`

`F_2=m/(4r)*"v"^2/4=1/16(mv^2)/r=F_1/16`

`thereforeF_1-F_2=F_1-F_1/16=15/16F_1`