A) \[\text{2}.\text{86 m}/{{\text{s}}^{\text{2}}}\]
B) \[\text{1}.\text{65 m}/{{\text{s}}^{\text{2}}}\]
C) \[\text{8}.\text{65 mi}{{\text{s}}^{\text{2}}}\]
D) \[\text{5}.\text{16 m}/{{\text{s}}^{\text{2}}}\]
Correct Answer: B
Solution :
Acceleration due to gravity\[,\]\[g=\frac{GM}{{{R}^{2}}}\] At earth,\[{{g}_{e}}=\frac{G{{M}_{e}}}{{{R}_{e}}^{2}},\] and at moon,\[{{g}_{m}}=\frac{G{{M}_{m}}}{{{R}_{m}}^{2}}\] \[\therefore \] \[\frac{{{g}_{e}}}{{{g}_{m}}}=\frac{{{M}_{e}}}{{{M}_{m}}}{{\left( \frac{{{R}_{m}}}{{{R}_{e}}} \right)}^{2}}\] \[\Rightarrow \] \[{{g}_{m}}={{g}_{e}}\times \frac{{{M}_{m}}}{{{M}_{e}}}\times {{\left( \frac{{{R}_{e}}}{{{R}_{m}}} \right)}^{2}}\] \[=9.8\times \frac{1}{81}\times 3.7\times 3.7\] \[=1.65\,\,meter/{{\sec }^{2}}\]
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