A) 400 N
B) 800 N
C) 500 N
D) 200 N
Correct Answer: A
Solution :
Here, weight of body on earth \[{{\omega }_{e}}=700N\] Mass of the planet \[{{M}_{P}}=\frac{{{M}_{e}}}{7}\] Radius of the planet \[{{R}_{P}}=\frac{{{R}_{e}}}{2}\] The relation for the value of (g) is \[g=\frac{GM}{{{R}^{2}}}\propto \frac{M}{{{R}^{2}}}\] Hence , \[\frac{{{g}_{e}}}{{{g}_{p}}}=\frac{{{M}_{e}}}{{{M}_{p}}}\times \frac{{{({{R}_{P}})}^{2}}}{{{({{R}_{e}})}^{2}}}\] \[=\frac{{{M}_{e}}}{\frac{{{M}_{e}}}{7}}\times \frac{{{\left( \frac{1}{2}{{\operatorname{Re}}^{2}} \right)}^{2}}}{{{({{R}_{e}})}^{2}}}=\frac{7}{4}\] or \[{{g}_{p}}=\frac{4}{7}ge\] So, weight of body on the planet is given by \[=\frac{4}{7}\times \] weight of body on earth \[=\frac{4}{7}\times 700=400N\]
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