The radius of a Planet A is half the radius of planet B. If the mass of A is Ma, what 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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heya frnd
According to law of Gravitation:
F = GmM/(R^2)
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
According to law of Gravitation:
F = GmM/(R^2)
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
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