Question

the radius of the 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

Answer 1

The  mass of planet B would be two times the mass of planet A.

Explanation:

According to law of Gravitation:

                    g = $\frac{GM}{R^{2} }$                                                                                      Where, G - gravitational constant, M - mass of planet and R - radius of the planet.  Then the value of M will be

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

According to question  

           $\frac{g_{b} }{g_{a} } = \frac{1}{2}$   and     $\frac{R_{b} }{R_{a} } = 2$

therefore, according to the formula of mass shown above

           $\frac{M_{b} }{M_{a} } = \frac{g_{b} }{g_{a} }(\frac{R_{b} }{R_{a} })^{2}$  

            $\frac{M_{b} }{M_{a} } = \frac{1}{2}(2^{2})$

            $M_{b} = 2M_{a}$,  Where Mb is the mass of planet B and Ma is the mass of planet B.

 Then the mass of planet B should be two times the mass of planet A.

Answer 2

Answer:

The mass of planet B must be twice that of the planet A.

Explanation:

See the attachment.