A mass of `6xx10^(24) kg` is to be compressed in a sphere in such a way that the escape velocity from its surface is `3xx10^(8) m//s`. Find the radius of the sphere (in `mm`).

Options

A. 9 mm
B. 9cm
C. 9 km
D. 9m

Answer

A

Explanation

Escape velocity, `v_(e)=sqrt((2GM)/(R ))`
In this case R is the radius and M is the mass of the sphere and not of the earth.
`therefore v_(e)=3xx10^(8)=sqrt((2xx6.67xx10^(-11)xx6xx10^(24))/(R ))`
Squaring both sides we get
`9xx10^(16)=(12xx6.67xx10^(13))/(R )`
`therefore R=(12xx6.67xx10^(13))/(9xx10^(16))=8.89xx10^(-3)div 9 mm`