Question

The radius of planet A is half the radius of planet B. If the mass of A is
Mwhat must be the mass of B so that the value of g on B is half that of
its value on A​

Answer 1

Answer:

Acceleration due to gravity is the force with which a planet or celestial object attracts an object divided by the mass of the object.

According to law of Gravitation:

F = GmM/(R^2)

Where, G - gravitational constant, M - mass of planet, m - mass of the object and R - radius of the planet.

F/m = g = GM/(R^2)

Ra = Rb/2 and ga = 2*gb

Taking the ratio of both the g's;

ga/gb = (Ma/Mb)/[(Ra/Rb)^2]

2 = (Ma/Mb)/[(1/2)^2]

(Ma/Mb)= 2*(1/4)

(Ma/Mb) = 1/2

Therefore, mass of planet B should be two times the mass of planet A to have an acceleration due to gravity half of that of planet A.