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A brass wire of length 4.5m with cross-s...

A brass wire of length 4.5m with cross-section area of `3xx10^(-5) m^2` and a copper wire of length 5.0 m with cross section area `4xx10^(-5) m^2` are stretched by the same load. The same elongation is produced in both the wires. Find the ratio of Young’s modulus of brass and copper.

Text Solution

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For brass,
`L_B = 4.5m , A_B = 3 xx 10^(-5) m^2`
`l_B = l, F_B = F`
`Y_B = (F_B L_B)/(A_B l_B)`
` therefore Y_B = (F xx 4.5)/(3 xx 10^(-5) xx l)`
For copper,
`Y_C = (F_C L_C)/(A_C l_C)`
` therefore Y_c = (F xx 5.0)/(4 xx 10^(-5) xx l)`
`(Y_B)/(Y_C) = (F xx 4.5)/(3 xx 10^(-5) xx l) xx (4 xx 10^(-5) xx l)/(F xx 5)`
` = (18 xx 10^(-5))/(15 xx 10^(-5)) = 1.2`
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