A) Zero
B) \[3.85\times {{10}^{7}}m\]
C) \[8\times {{10}^{8}}m\]
D) \[3.46\times {{10}^{8}}m\]
Correct Answer: B
Solution :
Let x be the distance of the point from the centre of earth whose gravitational intensity is zero. Therefore,\[\frac{G{{M}_{e}}}{{{x}^{2}}}=\frac{GMm}{{{(3.85\times {{10}^{8}}-x)}^{2}}}\] \[\frac{x}{(3.85\times {{10}^{8}}-x)}=\sqrt{\frac{{{M}_{e}}}{{{M}_{m}}}}=\sqrt{\frac{5.98\times {{10}^{24}}}{7.35\times {{10}^{22}}}}=9\] \[\frac{x}{9}+x=385\times {{10}^{8}}\] \[x=\frac{9\times 385\times {{10}^{8}}}{10}\]\[x=3.46\times {{10}^{8}}m\] Distance from moon \[=3.85\times {{10}^{8}}-3.46\times {{10}^{8}}\] \[=3.9\times {{10}^{7}}m\]
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