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Atoms And Molecules

Question
CBSEENSC9006100

The mass of the earth is 6 x 1024 kg and that of the moon is 7.4 x 1022 kg. If the distance between the earth and the moon be 3.84 x 105 km, calculate the force exerted by the earth on the moon. The value of G = 6.7 x 10–11 Nm2 kg–2.

Solution

Given semicolon
space space The space mass space of space the space earth comma space straight M space equals space 6 space cross times space 10 to the power of 24 kg
space The space space mass space of space the space moon comma space straight m space equals space 7.4 space cross times space 10 to the power of 22 kg 
The distance between the earth and the moon is, 
                    r = 3.84 x 105 m
                      = 3.84 x 105 x 1000 m
                      = 3.84 x 108 m
The value of G = 6.7 x 10-11 Nm2 kg-2

The force exerted by the earth on the moon is, 

straight F space equals space straight G Mm over straight r squared
space equals fraction numerator 6.7 space cross times space 10 to the power of negative 11 end exponent cross times 6 space cross times space 10 to the power of 24 space cross times space 7.4 space cross times 10 to the power of 22 over denominator left parenthesis 3.84 space cross times space 10 to the power of 8 right parenthesis squared end fraction
equals 2.01 space cross times space 10 to the power of 20 straight N 

Thus the force exerted by the earth on the moon is 2.01 x 1020 N.