A) 400 N
B) 300 N
C) 200 N
D) 100 N
Correct Answer: A
Solution :
Here: weight of object on earth \[{{\omega }_{e}}=700\,N\] Mass of the planet \[{{M}_{p}}=\frac{{{M}_{e}}}{7}\] (where \[{{M}_{e}}\] is mass of earth) Radius of planet \[{{R}_{p}}=\frac{{{R}_{e}}}{2}\] (where \[{{R}_{e}}\] is radius of earth) From the formula \[g=\frac{GM}{{{R}^{2}}}\propto \frac{M}{{{R}^{2}}}\] Hence, \[\frac{{{g}_{e}}}{{{g}_{p}}}=\frac{{{M}_{e}}}{R_{e}^{2}}\times \frac{R_{p}^{2}}{R_{e}^{2}}=\frac{{{M}_{e}}}{\frac{1}{2}{{M}_{e}}}\times \frac{{{\left( \frac{1}{2}{{R}_{e}} \right)}^{2}}}{{{({{R}_{e}})}^{2}}}=\frac{7}{4}\] So, \[{{g}_{p}}={{g}_{e}}\times \frac{7}{4}\] Hence, weight of object on planet will be \[=\frac{4}{7}\times \]weight on earth \[=\frac{4}{7}\times 700=400\,N\]
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