A) 100 N
B) 200 N
C) 450 N
D) 900 N
Correct Answer: B
Solution :
Here: mass of planet \[{{M}_{p}}=\frac{{{M}_{e}}}{9}\] where \[{{M}_{e}}\]mass of earth is. weight of the body on earth \[{{w}_{e}}=450\,N\] radius of the planet \[{{R}_{p}}=\frac{{{R}_{e}}}{2}\] (where \[{{R}_{e}}\] is radius of earth) From the law of gravitation that weight of the body \[w=\frac{GMm}{{{R}^{2}}}\Rightarrow w\propto \frac{M}{{{R}^{2}}}\] Hence, \[\frac{{{w}_{e}}}{{{w}_{p}}}=\frac{{{M}_{e}}}{{{M}_{p}}}\times {{\left( \frac{{{R}_{p}}}{{{R}_{e}}} \right)}^{2}}\] or \[\frac{450}{{{w}_{p}}}=\frac{{{M}_{e}}}{\left( \frac{{{M}_{e}}}{9} \right)}\times \frac{{{\left( \frac{{{R}_{e}}}{2} \right)}^{2}}}{R_{e}^{2}}\] so, \[{{w}_{p}}=\frac{450\times 4}{9}=200N\]
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