question_answer

On the earth, a Sumo of 400 kg is checking his reading on a spring balance. To have the same reading of spring balance on the moon, 6 Sumos of mass 400 kg each should stand on it. Explain, (\[\text{g}=\text{1}0\text{m}{{\text{s}}^{-\text{2}}}\])

Answer:

Case (i): Given, mass of the sumo on the earth, \[{{m}_{Earth}}=400kg\] Weight of the sumo on the Earth = ? We know, \[{{w}_{Earth}}={{m}_{Earth}}\times {{g}_{Earth}}\] \[\Rightarrow 400\times 10=4000\,N\] Case (ii): Given, mass of the sumo on the Moon, \[{{m}_{Moon}}=400kg\] Weight of the sumo on the Moon, \[{{m}_{Moon}}=?\] We know, \[{{W}_{Moon}}={{m}_{Moon}}\times {{g}_{Moon}}\] \[{{w}_{Moon}}=400\times \frac{10}{6}=666.6N\] \[\left( \because {{g}_{Earth}}=\frac{{{g}_{Moon}}}{6} \right)\] To get 4000 N weight on the Moon, the number of sumos \[=x\] Now, we have to find\['x'.\] \[x=\frac{weight\,\,of\,\,thesumoon\,\,the\,\,Earth}{weight\,\,of\,\,the\,\,sumo\,\,on\,\,the\,\,Moon}=\frac{4000}{666.6}=6\] Therefore, to get the same 4000 N weight on the Moon 6 sumos are required.