The radius of 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 of A?


Suppose the radius of planet A= RA And radius of planet B = RB And

Mass of planet A = MA, then find mass of planet B = MB.

Here, RA= RB/2, gB= ½ gA

Then, g= GM / R2 And gA = GMA /R2A

Therefore, gB = G MB/ R2B

Now, MB/ R2-B = ½ [GMA /(RB/2)2]

MB/ R2B= ½ [4 (GMA /(RB)2)]

So, MB= 2MA

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