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

Answer:

0.2 milisecond

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

$\frac{2}{5}(2M)\times R^{2}\times \frac{2\pi }{T}=\frac{2}{5}(2M)\times R'^{2}\times \frac{2\pi }{T'}$

$\frac{R^{2}}{T}=\frac{R'^{2}}{T'}$

$T'=\frac{R'^{2}T}{R^{2}}$

$T'=\frac{10\times 10\times10}{7\times10^{5}\times 7\times 10^{5}}$

T' = 2.04 x 10^-9 days

T' = 0.2 milisecond