A) 200 g wt.
B) 400 g wt.
C) 50 g wt.
D) 300 g wt.
Correct Answer: B
Solution :
Weight at earths surface w = mg Acceleration due to gravity at earths surface \[g=\frac{G{{M}_{e}}}{R\,_{e}^{2}}\] For planet, \[g=\frac{G{{M}_{e}}}{R{{\,}^{2}}}=\frac{G{{M}_{e}}/7}{{{({{R}_{e}}/2)}^{2}}}\] \[=\frac{4}{7}\frac{G{{m}_{e}}}{R\,_{e}^{2}}=\frac{4}{7}g\] \[\therefore \] Weight at the surface of planet=mg \[=m\left( \frac{4g}{7} \right)\] \[=\frac{4}{7}mg=\frac{4}{7}\times 700\] \[=400\,g\,wt.\]
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