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

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

Step-by-step 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(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(m.M_A)/((2r)^2) =G(m.M_B)/((r)^2)`

`(M_A)/(4r^2) =(M_B)/(r^2)`

`M_A=4M_B`