the radius of planet a is half the radius of planet be the mass of a is M A what must be the mass of B so that the value of g on the is half that of its value on A​

M_b = 2M_a

Explanation:

From gravity equation, we know that;

g = GM/R²

Where;

g is acceleration due to gravity

G is the gravitational constant

M is mass

Thus, making mass(M) the subject, we have;

M = gR²/G

Since we want to find the mass of B so that value of g on B is half that of its value on A.

Thus;

> g_b = ½g_a

> g_b/g_a = ½

Also, we are told that;

> R_a = ½R_b

> R_b/R_a = 2

If M_a = g_a•R_a²/G

And M_b = g_b•R_b²/G

Thus;

M_b/M_a = (g_b•R_b²/G)/(g_a•R_a²/G)

G will cancel out to give;

M_b/M_a = (g_b•R_b²)/(g_a•R_a²)

Rearranging for ease of simplification, we have;

M_b/M_a = (g_b/g_a) × (R_b/R_a)²

Plugging in the relevant ratios gives;

M_b/M_a = ½ × 2²

M_b/M_a = 2

M_b = 2M_a

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