A) \[\frac{4\pi G}{3g\,R}\]
B) \[\frac{3\pi G}{4g\,R}\]
C) \[\frac{3g}{4\pi RG}\]
D) \[\frac{\pi RG}{2g}\]
Correct Answer: C
Solution :
When the earth in supposed to be a sphere of mean density p, then mass of the earth is will be: \[M=\frac{4}{3}\,\pi {{R}^{3}}\rho \] \[\rho =\frac{3M}{4\pi {{R}^{3}}}\] ??(i) Also, from the formula \[g=\frac{GM}{{{R}^{2}}}\] ??(ii) Hence from equations (i) and (ii), we have. \[\rho =\frac{3g}{4\pi \,GR}\]
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