Answer:
Case (i) : Given, weight of the sugar on the Earth, \[{{w}_{Earth}}=50N\] We know, \[{{w}_{Earth}}={{m}_{Earth}}\times {{g}_{Earth}}\] \[\Rightarrow 50N={{m}_{Earth}}\times 10\,m{{s}^{-2}}\] \[\Rightarrow {{m}_{Earth}}=\frac{50}{10}=5kg\] And also given on Earth for \[100g=\frac{100}{1000}=0.1kg\] of sugar - 10 cups of tea can be made For 5 kg, how many cups can be made? \[\Rightarrow \frac{0.1kg}{5kg}=\frac{10}{x}\] \[\Rightarrow x\times 0.1=10\times 5\] \[\Rightarrow x=\frac{50}{0.1}=500\,cups\] Therefore, for 5 kg mass of sugar on the Earth we can make 500 cups Case (ii): Given, weight of the sugar on the Moon, \[{{w}_{Moon}}=50N\] We know, \[{{w}_{Moon}}={{m}_{Moon}}\times {{g}_{Moon}}\] \[\Rightarrow 50N={{m}_{Moon}}\times \frac{10}{6}m{{s}^{-2}}\,\,\left( \because {{g}_{Earth}}\frac{{{g}_{Moon}}}{6} \right)\] \[\Rightarrow {{m}_{Moon}}\frac{300}{10}=30kg\] And also given on the Moon for \[100g=\frac{100}{1000a}=0.1\] kg of sugar - 10 cups of tea can be made For 30 kg how many cups can be made? \[\Rightarrow \frac{0.1kg}{30kg}=\frac{10}{x}\] \[\Rightarrow 0.1\times x=30\times 10\Rightarrow \frac{300}{0.1}=3000\,cups\] From the cases, we can observe that on the Moon we can make more number of cups.
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