A) \[R/4\]
B) \[R/4\]
C) \[R/3\]
D) \[R/8\]
Correct Answer: B
Solution :
We know that \[g=\frac{Gm}{{{R}^{2}}}=\frac{G}{{{R}^{2}}}\left[ \frac{4}{3}\pi \,{{R}^{3}}d \right]\] Where, d = mean density of earth. For planet, \[g'=\frac{G}{{{(R')}^{2}}}\times \left[ \frac{4}{3}\pi {{R}^{+3}}(2d) \right]\] Given that \[g=g'\] Therefore, \[\frac{G}{{{R}^{2}}}\left[ \frac{3}{4}\,\pi {{R}^{3}}d \right]=\frac{G}{{{(R')}^{2}}}\times \frac{4}{3}\pi {{R}^{'3}}(2d)\] Solving, we get, \[R'=(R/2)\]
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