A small mass attached to a strong rotates on a frictionless table top as shown . 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. decreases by a factor of 2
B. remain constant
C. increases by a factor of 2
D. increase by a factor of 4

Answer

D

Explanation

According to law of conservation of angular momentum
`mvr = mv.r.` or `vr = v. ((r)/(2))` or `v. = 2v " " ….. (i)`
`therefore (K)/(K..) = ((1)/(2) mv^(2))/((1)/(2) mv.^(2)) = ((v)/(v.))^(2) = 4 , K. =4 K` (Using (i))