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
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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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