Answer: It takes the moon 27.3 days to complete one revolution around the earth.
Step-by-step explanation:
(i) The force that acts on the moon is the gravitational force between the moon and the earth, given by the equation F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the earth and the moon, respectively, and r is the distance between the two objects. According to Newton's third law of motion, for every action there is an equal and opposite reaction. In this case, the earth pulls the moon towards it with the gravitational force, and the moon exerts an equal and opposite force on the earth.
(ii) To find the time for one complete revolution of the moon about the earth, we can use the equation T = 2π * √(r^3 / (G * M)), where T is the period of revolution, r is the radius of the orbit, G is the gravitational constant, and M is the mass of the earth. Plugging in the given values, we get:
T = 2π * √(400,000 km^3 / (G * M))
T = 2π * √(400,000,000,000 m^3 / (6.67 × 10^-11 Nm^2/kg^2 * 5.97 × 10^24 kg))
T = 2π * √(67,000,000,000,000 s^2)
T = 27.3 days
So, it takes the moon 27.3 days to complete one revolution around the earth.