Question

The radius of the moon is approximately 3.7 times smaller than the radius of the earth. Assuming that their densities are same, what is the escape velocity of the moon compared to earth?

(a) 0.07 times

(b) 0.7 times

(c) 7 times

(d) 3.7 times

I had been asked this question in examination.

This key question is from Gravitation topic in division Gravitation of Physics – Class 11

Answer 1

Correct answer is (a) 0.07 times

The explanation is: Escape velocity (v) = [(2*G*M)/R]^1/2

Mass of moon = (Density) x (Volume)

 = (Density) x (Volume of the earth)/50.65;

[Volume is directly proportional to the cube of the radius]

Vmoon/vearth = [(2*G*Mmoon)/Rmoon^1/2/[(2*G*Mearth)/Rearth]^1/2

 = [1/(50.65 x 3.7)] ^½

 = 0.07

Therefore; Vmoon = 0.07 (vearth).