Question

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

• A. $3.8 \times 10^8\, m$
• B. $3.37 \times 10^6\, m$
• C. $7.60 \times 10^4\, m$
• D. $1.9 \times 10^2\, m$

Answer 1

The Correct Option is A

Here, Potential energy of system, $U = - 7.79 \times 10^{28}\, J$ Mass of the earth, $M_E = 6 \times 10^{24}\, kg$ Mass of the moon, $M_M = 7.4 \times 10^{22}\, kg$ The potential energy of the earth-moon system is $U = -\frac{GM_{E}M_{M}}{r}$ where $r$ is the mean distance between earth and moon. $\therefore r = -\frac{GM_{E}M_{M}}{U}$ $= -\frac{6.67 \times10^{-11}\times 6\times 10^{24}\times 7.4\times 10^{22}}{-7.79 \times 10^{28}}$ $= 3.8\times 10^{8}\,m$