A small mass attached to a string rotates on a frictionless table top as shown in Fig. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will

Options

A. increase by a factor of `4`
B. decrease by a factor of `2`
C. remain constant
D. increase by a factor of `2`

Explanation

`mvr=mv'(r )/(2)implies v'=2v`
`K=(1)/(2)mv^(2), K'=(1)/(2)mv'^(2)=(1)/(2)m(2v)^(2)`
`(K')/(K)=4`