Question

collapse the star had a mass of 2 times the mass of the Sun and a radius the same as the sun. Before the collapse it rotates once every 10 days. After the collapse it has not lost any mass but now has a radius of only 10 km. What is its rotation rate in rev/s after the collapse

Answer 1

0.2 milisecond

Step-by-step explanation:

Let the mass of sun is M

mass of star = 2 M

initial radius of the star, R = radius of sun = 7 x 10^5 km

initial time period, T = 10 days

final radius, R' = 10 km

mass remains same.

As no external torque is acting on the star so its angular momentum remains constant.

So, Angular momentum before collapsing = Angular momentum after collapsing

I x ω = constant

`(2)/(5)(2M)* R^(2)* (2\pi )/(T)=(2)/(5)(2M)* R'^(2)* (2\pi )/(T')`

`(R^(2))/(T)=(R'^(2))/(T')`

`T'=(R'^(2)T)/(R^(2))`

`T'=(10* 10*10)/(7*10^(5)* 7* 10^(5))`

T' = 2.04 x 10^-9 days

T' = 0.2 milisecond