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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 - Science and Technology 1

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Numerical

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

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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.

Concept: Gravitation
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