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Physics Question on Gravitation

The mass of the earth is 6×1024 kg6 \times 10^{24}\, kg and that of the moon is 7.4×1022 kg7.4 \times 10^{22}\, kg. The potential energy of the system is −7.79×1028 J-7.79 \times 10^{28}\, J. The mean distance between the earth and moon is (G=6.67×10−11 N m2kg−2)(G = 6.67 \times 10^{-11}\, N\, m^2kg^{-2})

A

3.8×108 m3.8 \times 10^8\, m

B

3.37×106 m3.37 \times 10^6\, m

C

7.60×104 m7.60 \times 10^4\, m

D

1.9×102 m1.9 \times 10^2\, m

Answer

3.8×108 m3.8 \times 10^8\, m

Explanation

Solution

Here, Potential energy of system, U=−7.79×1028 JU = - 7.79 \times 10^{28}\, J Mass of the earth, ME=6×1024 kgM_E = 6 \times 10^{24}\, kg Mass of the moon, MM=7.4×1022 kgM_M = 7.4 \times 10^{22}\, kg The potential energy of the earth-moon system is U=−GMEMMrU = -\frac{GM_{E}M_{M}}{r} where rr is the mean distance between earth and moon. ∴r=−GMEMMU\therefore r = -\frac{GM_{E}M_{M}}{U} =−6.67×10−11×6×1024×7.4×1022−7.79×1028= -\frac{6.67 \times10^{-11}\times 6\times 10^{24}\times 7.4\times 10^{22}}{-7.79 \times 10^{28}} =3.8×108 m= 3.8\times 10^{8}\,m