A star of mass equal to two solar masses and radius `10^(6) km` rotates about its axis with an angular speed of `10^(-6)rad s^(-1)`. What is the angular speed of the star, when it collapses (due to inward gravitational forces) to a radius of `10^(4) km`?

Options

A. `10^(-1)"rad s"^(-1)`
B. `10^(-2)"rad s"^(-1)`
C. `10^(-3)"rad s"^(-1)`
D. `10^(-4)" rad s"^(-1)`

Answer

B

Explanation

Here, `R_(1)=10^(6)km, omega_(1)=10^(-6)"rad s"^(-1)`
`omega_(2)=?, R_(2)=10^(4)km`
`"As "I_(1)omega+(1)=I_(2)omega_(2)`
`therefore" "omega_(2)=(I_(1)omega_(1))/(I_(2))=((2)/(5)MR_(1)^(2)omega_(1))/((2)/(5)MR_(2)^(2))`
`omega_(2)=((R_(1))/(R_(2)))^(2)omega_(1)=((10^(6))/(10^(4)))^(2)xx10^(-6)=10^(-2)"rad s"^(-1)`