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7.Gravitation
easy
The mass of the earth is $6.00 \times {10^{24}}\,kg$ and that of the moon is $7.40 \times {10^{22}}\,kg$. The constant of gravitation $G = 6.67 \times {10^{ - 11}}\,N - {m^2}/k{g^2}$. The potential energy of the system is $ - 7.79 \times {10^{28}}\,joules$. The mean distance between the earth and moon is
A
$3.80 \times {10^8}\,metres$
B
$3.37 \times {10^6}\,metres$
C
$7.60 \times {10^4}\,metres$
D
$1.90 \times {10^2}\,metres$
Solution
(a) $U = – \frac{{GMm}}{r}$
$ \Rightarrow \,7.79 \times {10^{28}} = \frac{{6.67 \times {{10}^{ – 11}} \times 7.4 \times {{10}^{22}} \times 6 \times {{10}^{24}}}}{r}$
$ \Rightarrow \,\,r = 3.8 \times {10^8}\,m$
Standard 11
Physics
