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Question
The masses of the earth and moon are 6 × 1024 kg and 7.4 × 1022 kg, respectively. The distance between them is 3.8 × 105 km. Calculate the gravitational force of attraction between the two?
Use G = 6.7 × 10–11 N m2 kg–2
Solution
the mass of the earth, M = 6 × 1024 kg
the mass of the moon,
m = 7.4 × 1022
the distance between the earth and the moon,
d = 3.84 × 105 km
= 3.84 × 105 × 1000 m
= 3.84 × 108 m
G = 6.7 × 10-11 Nm2kg-2
the force exerted by the earth on the moon is
F = `("G" "M" xx "m")/"d"^2`
= `(6.7 xx 10^-11 "Nm"^2"kg"^-2 xx 6 xx 10^24 "kg" xx 7.4 xx 10^22 "kg")/(3.84 xx 10^8 "m")^2`
= `((6.7 xx 10^-11) xx (6 xx 10^24) xx (7.4 xx 10^22))/(3.84 xx 10^8)^2`
= `(6.7 xx 6 xx 7.4)/(3.84 xx 3.84) xx 10^19`
= 2 × 1020 N.
Thus the force exerted by the earth on the moon is 2 × 1020 N.
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