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Evgen [1.6K]
3 years ago
9

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 for

ce 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.
Physics
1 answer:
Dennis_Churaev [7]3 years ago
3 0

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

<u>As we know, gravitational force of attraction is given by:</u>

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

<em>According to the condition</em>

Force on m due toM_B=Force on m due toM_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

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