Answer:
M_b = 2M_a
Step-by-step 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