A) 6 N
B) 4 N
C) 2.25 N
D) I N
Correct Answer: B
Solution :
Weight of the object of mass m on earth \[{{W}_{e}}=m{{g}_{e}}=\frac{G{{M}_{e}}m}{R_{e}^{2}}\] ?(i) Weight of object of mass m on planet \[{{W}_{p}}=m{{g}_{p}}=\frac{G{{M}_{p}}m}{R_{p}^{2}}\] ?(ii) From Eqs. (i) and (ii) \[\frac{{{W}_{p}}}{{{W}_{e}}}=\frac{G{{M}_{p}}m}{r_{p}^{2}}\times \frac{R_{e}^{2}}{G{{M}_{e}}m}\] \[=\frac{{{M}_{p}}}{{{M}_{e}}}{{\left( \frac{{{R}_{e}}}{{{R}_{p}}} \right)}^{2}}\] ?(iii) \[\left( \begin{align} & \text{Given: }{{M}_{p}}=\frac{1}{9}{{m}_{e}} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{r}_{p}}=\frac{1}{2}{{R}_{e}} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{W}_{e}}=9N \\ \end{align} \right)\] \[\frac{{{W}_{p}}}{{{W}_{e}}}=\frac{\frac{1}{9}{{M}_{e}}}{{{M}_{e}}}\times {{\left( \frac{{{R}_{e}}}{1/2{{R}_{e}}} \right)}^{2}}\] \[{{W}_{p}}=\frac{4}{9}\times 9=4N\]
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