Answer:
We know that, \[W=mg\] \[\Rightarrow \] \[W\propto g\] (\[\because \]m is constant) \[\Rightarrow \] \[\frac{{{W}_{2}}}{{{W}_{1}}}=\frac{{{g}_{2}}}{{{g}_{1}}}\] How to get \[\frac{{{g}_{2}}}{{{g}_{1}}}?\] We know that,\[g=\frac{GM}{{{R}^{2}}}\]\[\Rightarrow \] \[g\propto \frac{M}{{{R}^{2}}}\] (\[\because \]G is constant) \[\Rightarrow \]\[\frac{{{g}_{2}}}{{{g}_{1}}}=\frac{{{M}_{2}}}{{{M}_{1}}}\times \frac{R_{1}^{2}}{R_{2}^{2}}=\frac{M/9}{M}\times \frac{{{(R)}^{2}}}{{{(R/2)}^{2}}}=\frac{4}{9}\] \[\therefore \]\[\frac{{{W}_{2}}}{{{W}_{1}}}=\frac{{{g}_{2}}}{{{g}_{1}}}=\frac{4}{9}\] \[\therefore \]\[{{W}_{2}}=\frac{4}{9}\times 9=4N\] Earth Planet \[{{M}_{1}}=M\] \[{{M}_{2}}=M/9\] \[{{R}_{1}}=R\] \[{{R}_{2}}=R/2\] \[{{W}_{1}}=9N\] \[{{W}_{2}}=?\]
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