A) \[\frac{1}{8}g\]
B) \[\frac{1}{2}g\]
C) \[\frac{1}{3}g\]
D) \[g\]
Correct Answer: B
Solution :
\[{{R}_{1}}={{R}_{1}};\,\,{{R}_{2}}=\frac{R}{2},\] \[{{m}_{1}}={{m}_{2}}=\frac{m}{8},\,\,{{g}_{1}}=g,\,\,{{g}_{2}}=?\] \[g=\frac{GM}{{{R}^{2}}}\Rightarrow \frac{{{g}_{1}}}{{{g}_{2}}}\times \frac{{{M}_{1}}}{{{M}_{2}}}\times \frac{R_{2}^{2}}{R_{1}^{2}}=\frac{m}{\frac{m}{8}}\times \frac{{{\left( \frac{R}{2} \right)}^{2}}}{{{R}^{2}}}=2\] \[\therefore {{g}_{1}}=\frac{g}{2}\]
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