# b. The radius of planet A is half the radius of planet B. If the mass of A is MA, what must be

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b. 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 on A?

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verified

g=$$GM\over R^2$$

$$M=\tfrac{gR^2}{G}$$

Acording to the given data , $$\tfrac{gB}{gA}=\tfrac{1}{2}$$

and $$\tfrac{{R_B}}{R_A}=2$$

$$\tfrac{M_B}{M_A}=\tfrac{g_B}{g_A}( \tfrac {R_B}{R_A})^2$$

$$\tfrac{M_B}{M_A}=\tfrac{1}{2}2^2$$

$$M_B=2M_A$$

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