Question

A spacecraft is launched from Earth toward the moon where will the spacecraft be when the gravitational forces acting on it are equal

A closer to earth than to the moon because the moon has greater mass than the earth

B closer to the moon because the moon greater mass than the earth

C closer to earth than to the moon because earth has greater mass

D Closer to moon than earth because earth has a greater mass than the moon

Answer 1

I would go with d makes more sense

Answer 2

Answer:

D Closer to moon than earth because earth has a greater mass than the moon

Explanation:

As we know that gravitational force is given by

$F = \frac{Gm_1m_2}{r^2}$

so here if the net gravitational force at some distance between moon and earth is zero or equal due to moon and earth then in that case

$F_{moon} = F_{earth}$

so here we can say

$\frac{GM_m m}{r_1^2} = \frac{GM_e m}{r_2^2}$

so here we will have

$\frac{M_m}{M_e} = \frac{r_1^2}{r_2^2}$

since mass of earth is more than mass of moon so we can say

$\frac{r_1}{r_2} < 1$

so here we have

$r_1 < r_2$

so the position is closer to moon because moon is of smaller mass than earth