# A star of mass 4 times the solar mass and radius 10^8 km rotates about its axis with an angular speed of 10^{-4} rad s^{-1}.

A star of mass 4 times the solar mass and radius 108 km rotates about its axis with an angular speed of 10-4 rad s-1. When the star collapses to a radius at 105 km then its angular speed is(Take solar mass = 1.99 x 1030 kg)(a) 10 rad s−1(b) 0.1 rad s−1(c) 102 rad s−1(d) 10−2 rad s-1

Answer is : (d) 10 −2 rad s -1 As total momentum remains conserved l 1 ω 1 = l 2 ω 2 $$\frac{2}{5}$$ MR 2 1 ω 1 =  $$\frac{2}{5}$$ MR 2 2 ω 2   $$\left[\because l=\frac{2}{5}MR^2\right]$$ ⇒ R 1 2 ω 1  = R 2 2 ω 2   ⇒ ω 2  =  $$\left(\frac{R_1}{R_2}\right)^2$$  x ω 1 =  $$\left(\frac{10^8}{10^5}\right)^2$$  x 10 -4 = 10 -2 rad s -1