Question

A mass of 6 × 1024 kg (equal to the mass of the earth) is to be compressed in a sphere in such a way that the escape velocity from its surface is 3 × 108 m s−1. What should be the radius of the sphere?

Answer 1

Answer:

r=1.2808*10^11m

Explanation:

escape velocity is

v=[2GM/R]^1/2

3*108=[2*6.67*10^-11*6*1024/R]^1/2

3*108*3*108/2*6.67*10^-11*6*1024=R

R=1.2808*10^11 meter

Answer 2

The sphere has the radius, 9mm.

Explanation:

The mass of the sphere is equal to the earth’s mass. This is done in such a way that from its surface, the escape velocity is $3 \times 108 m s^{-1}$.  

Sphere has the mass = $6 \times 10^{24} \mathrm{kg}$

Escape velocity = $3 \times 10^{8} m / s$

Escape velocity can be shown as $\text { ve }=2 \mathrm{GMR}$

$\Rightarrow R=2 G M v e 2$      

$=2 \times 6.67 \times 10^{-11} \times 6 \times 10243 \times 1082$

$=8.89 \times 10^{-3} \mathrm{m}$

$=9 \mathrm{mm}.$