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

Answer

C

Explanation

( c) Initial kinetic energy of mass
`K_(inital) = (1)/(2) I omega^2 = (1)/(2) (mr^2) omega^2 = (1)/(2) m(r^2 omega^2)`
=`(1)/(2) mv_0^2`
Conservation of angular momentum
`m v_0 R_0 = mv (R_0)/(2) rArr v = 2 v_0`
Final kinetic energy of mass
`K_(final) = (1)/(2) mv^2 = (1)/(2)m(2 v_0)^2 = 4.(1)/(2) m_0^2 = 4 k_("initial")`.