Question

Escape velocity of a body from the earth's surface is 11.2km / sec. If the mass of the moon is 1/40 of the earth's mass and the radius of the moon is 1 / 8th of the radius of the earth. find escape velocity from the moon's surface.

Answer 1

I'm sorry for the answer being scattered, but hope you can understand. The calculations are all done in the attached files and the rest is typed.


Let, the mass of the earth be M and its radius is R. The force of gravity on a body of mass m at a distance x from the centre of the earth is (GMm)/x^2.
For a small displacement dx of the body against this force of gravity, the work done will be (GMm)/x^2 × dx.
Hence the work done to displace the body frim the earth surface to an infinite distance will be GMm/R.
If the escape velocity from earth is v, then the kinetic energy of the body is
$m {v}^{2} \times \frac{1}{2}$
This kinetic energy will be responsible for the work done by the body.
so, v= √(2GM/R).

Now. let the excape velocity at moon be vm and on earth's surface, let it be ve.