Question

The ratio of the radius of a planet A to that of a planet B is “r”. The ratio of acceleration due to gravity on the planets is “p”. The ratio of escape velocities of the two planets is _____

(a) (pr)^1/2

(b) (p/r)^1/2

(c) (pr)

(d) (p/r)

I had been asked this question in a national level competition.

Origin of the question is Gravitation topic in chapter Gravitation of Physics – Class 11

Answer 1

The correct choice is (a) (pr)^1/2

The best explanation: Escape velocity (v) = (2*g*R)^1/2

g = Acceleration due to gravity

R = Radius of planet

Given;

 Ra/Rb = r

 ga/gb = p

va/vb = (2*ga*Ra])^1/2/(2*gb*Rb) ^1/2

 = (p x r)^1/2.