Question

derive weight on moon=1/6 of weight on earth

Answer 1

$= \frac{g \: of \: earth \times m}{g \: of \: moon \times m} \\ = \frac{ \frac{6.674 \times {10}^{ - 11} \times 5.972 \times {10}^{24} }{ {(6.3781 \times {10}^{6} )}^{2} } }{ \frac{6.647 \times {10}^{ - 11} \times 7.347 \times {10}^{22} }{ {(1.738 \times {10}^{6} )}^{2} } } \\ = \frac{ \frac{39.857 \times {10}^{13} }{44.060 \times {10}^{12} } }{ \frac{49.033 \times {10}^{11} }{3.020 \times {10}^{12} } } \\ = \frac{0.9046 \times 10}{16.236 \times {10}^{ - 1} } \\ = \frac{9.046}{1.6236} \\ = \frac{5.571}{1} or \: 6 : 1$
This proves that Weight on earth is six times greater than on moon.