Question

the radius of planet A is half the radius of planet B if the mass of A is M suffix A what must be the mass of B so that the value of g on B is half that of its value on A?

Answer 1

Hey!!!

Here is your 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.

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Hope this answer wil help u....