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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.

Respuesta :

Answer:

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

Explanation:

Let's assume the:

  • mass of the object = [tex]m\,kilogram[/tex]
  • mass of the moon A = [tex]M_A\,kilogram[/tex]
  • mass of the moon B = [tex]M_B\,kilogram[/tex]
  • distance between the center of masses of the object and moon B = [tex]r\,meters[/tex]

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 = [tex]2r\,meters[/tex]

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

[tex]F=G\frac{m_1.m_2}{r^2}[/tex]

According to the condition

Force on m due to[tex]M_B=[/tex]Force on m due to[tex]M_A[/tex]

[tex]G\frac{m.M_A}{(2r)^2} =G\frac{m.M_B}{(r)^2}[/tex]

[tex]\frac{M_A}{4r^2} =\frac{M_B}{r^2}[/tex]

[tex]M_A=4M_B[/tex]

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