Question

The mass of the earth is `6xx10^(24)kg` and that of the moon is `7.4xx10^(22)kg`. The potential energy of the system is `-7.79xx10^(28)J`. The mean distance between the earth and moon is `(G=6.67xx10^(-11)Nm^(2)kg^(-2))`
A. `3.8xx10^(8) m`
B. `3.37xx10^(6)` m
C. `7.60xx10^(4)` m
D. `1.9xx10^(2)` m

Answer 1

Correct Answer - A
(a) Here, Potential energy of system,
`U= -7.79xx10^(28)J`
Mass of the earth, `M_(E)=6xx10^(24)kg`
Mass of the moon, `M_(M)=7.4xx10^(22) kg`
The potential energy of the earth-moon system is
`U=-(GM_(E)M_(M))/( r)`
where r is the mean distance between earth and moon.
`:. r= - (GM_(E)M_(M))/(U)=-(6.67x10^(-11)xx6xx10^(24)xx7.4 xx 10^(22))/(-7.79xx10^(28))`
`=3.8xx10^(8) m`