Question

A space probe is directly between two moons of a planet. If it is twice as far from moon A as it is from moon B, but the net force on the probe is zero, what can be said about the relative masses of the moons? a. Moon A is twice as massive as moon B. b. Moon A has the same mass as moon B. c. Moon A is four times as massive as moon B. d. Moon A is half as massive as moon B.

Answer 1

Answer:

c. Moon A is four times as massive as moon B

Explanation:

Let's assume the:

• mass of the object = $m\,kilogram$

• mass of the moon A = $M_A\,kilogram$

• mass of the moon B = $M_B\,kilogram$

• distance between the center of masses of the object and moon B = $r\,meters$

According to the given condition the object is twice as far from moon A as it is from moon B

• ∴distance between the center of masses of the object and moon B = $2r\,meters$

As we know, gravitational force of attraction is given by:

$F=G\frac{m_1.m_2}{r^2}$

According to the condition

Force on m due to$M_B=$Force on m due to$M_A$

$G\frac{m.M_A}{(2r)^2} =G\frac{m.M_B}{(r)^2}$

$\frac{M_A}{4r^2} =\frac{M_B}{r^2}$

$M_A=4M_B$