Question

Certain neutron stars (extremely dense stars) are believed to be rotating at about 1.6 rev/s. If such a star has a radius of 48 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation?

Answer 1

Mass,
`M=4.24* 10^9\ kg`

Step-by-step explanation:

Given that,

Angular velocity of the star,
`\omega=1.6\ reav/s`

Radius of the star, r = 48 cm = 0.48 m

The centripetal force acting on the on the star is caused by the gravitational force such that,

`(GMm)/(r^2)=(mv^)/(r)`

`(GM)/(r)=v^2`

Since,
`v=r\omega`

`M=(r^3\omega^2)/(G)`

`M=((0.48)^3* (1.6)^2)/(6.67* 10^(-11))`

`M=4.24* 10^9\ kg`

So, the minimum mass so that material on its surface remains in place during the rapid rotation is
`4.24* 10^9\ kg`