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The mas of the earth is 6 xx 10^(24)kg a...

The mas of the earth is `6 xx 10^(24)kg` and that of the moon is `7.4 xx 10^(24)kg`. If the distance between the centres of the earth and the moon is `3.84 xx 10^(5)km`, calculate the force exerted by the earth of the moon. `G=6.7 xx 10^(-11)Nm^(2) kg^(-2)`.

Text Solution

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The mass of the earth.
`M_(e)=6 xx 10^(24)Kg`
The mass of the moon,
`M_m=7.4 xx 10^(22)kg`
The distance between the centres of the erath and the moon.
`d=3.84 xx 10^(5)km`
`=3.84 xx 10^(5) xx 1000m`
`=3.84 xx 10^(8)m`
`G=6.7 xx 10^(-11)Nm^(2) kg^(-2)`
The force exerted by the earth on the moon is `F=G (M_e xx M_m)/(d^(2))`
`=(6.7xx 10^(-11)N m^(2) kg^(-2) xx 6 xx 10^(24) kg xx7.4 xx 10^(22)kg)/((3.84 xx 10^(8)m)^(2))`
`=2.01 xx 10^(20)N`
Thus, the force exerted by the earth on the moon is `2.01 xx 10^(20)N.`
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