C)
Explanation
the weigth of a mass is given by the formula
[tex]\begin{gathered} \text{Weigth(w)}=\text{mass(m)}\cdot(\text{acceleration due to gravity)(g)} \\ w=mg \end{gathered}[/tex]
we already now, that the acceletion of gravity is bigger in the earth than in the moon ( because it depens on the mass, and the earth has very more mass than the moon)
so, for the moon we have
[tex]\begin{gathered} w_m=m_m\cdot g_m \\ \text{isolate m}_m \\ m_m=\frac{w_m}{g_m} \end{gathered}[/tex]
now, when the mass in in the earth
[tex]\begin{gathered} w_e=m_e\cdot g_e \\ m_e=\frac{w_e}{g_e} \end{gathered}[/tex]
now, if we compare the masses ,equal ratios
[tex]\begin{gathered} m_m?m_e \\ \frac{w_m}{g_m}=\frac{w_e}{g_e} \end{gathered}[/tex]
we can see a ration of the weigth and g, as w depens on g, we can replace
[tex]\begin{gathered} \frac{m_m\cdot g_m}{g_m}=\frac{m_e\cdot g_e}{g_e} \\ m_m=m_e \end{gathered}[/tex]
we can conclude mass is the amount of matter in an object and does not change with location
If an object is moved to a location of greater gravitational force, , its weight will increase, but mass still remains the same.
so, the answer is
[tex]C)m_m=m_e[/tex]
I hope this helps you
