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A steel rod of cross-sectional area `16 cm^(2)` and two brass rods each of cross-sectional area `10 cm^(2)` together support a load of `5000 kg ` as shown in the figure. ( Given, `Y_(steel) = 2xx10^(6) kg cm^(-2) and Y_(brass) = 10 ^(6) kg cm^(-2))`. Choose the correct option(s). A. Stress in brass rod`=121 kg cm^(-2)`B. Stress in steel rod`=161 kg cm^(-2)`C. Stress in brass rod `=141 kg cm^(-2)`D. Stress in steel rod `=141 kg cm^(-2)` |
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Answer» Correct Answer - A::B Area of steel rod , `A_(S) = 16 cm^(2) ` ltbr. Area of two brass rods , `A_(B) = 2xx10 = 20 cm^(2)` `F = 5000 kg` ` sigma_(S) =` Stress in steel and ` sigma_(B) =` Stress in brass Decrease in length of steel rod = Decrease in length of brass rod ` (sigma_(S))/(Y_(S)).L_(S) = (sigma_(B))/(Y_(B)).L_(B)` `rArr sigma_(S) = Y_(S)/(Y_(B)).(L_(B))/(L_(S)). sigma_(B)` or ` sigma_(S) = ((2xx10^(6))/10^(6))(20/30)sigma_(B)` `sigma_(S) = 4/3sigma_(B)` ...(i) Now, ` F = sigma_(S)A_(S) +sigma_(B)A_(B)` or `5000 = sigma_(S)xx16+sigma_(B)xx20` ...(ii) From Eqs. (i) and (ii) , we get `sigma _(B) = 120.9 kg cm^(-2)` ` sigma_(S) = 161.2 kg cm^(-2)` |
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