b. The radius of planet A is half the radius of planet B. If the mass of A is M_{A,} what must be the mass of B so that the value of g on B is half that of its value on A?

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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