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).

Options

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)`

Answer

A, B

Explanation

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)`