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Two exactly similar wires of steel and c...

Two exactly similar wires of steel and copper are stretched by equal forces. If the total elogation is 1cm. Find by how much is each wire elongated ? Given Y for steel ` = 20 xx 10^(11) dyn e//cm^2 and Y for copper = 12xx10^(11) dyn e//cm^2`

A

Steel wire is elongated by 3/8 cm

B

Copper wire is elongated by 7/8 cm.

C

Steel wire is elongated by 5/8 cm.

D

Copper wire is elongated by 5/8 cm.

Text Solution

Verified by Experts

The correct Answer is:
A, D
Let l and A be the length and area of cross section of both the wire
if `Delta l_S` and `Delta l_C` are the elongation.s of the steel and copper wire respectively , then
`Y_S = F/A xx (l)/(Delta l_S) …..(i) " and " Y_C = F/A = (l)/(Delta l_C) ` ....(ii)
where `Y_S` and `Y_C` are the Young.s modulus of steel and copper wire respectively, F is the stretching force which is same in both the wires. From (i) and (ii) we get,
`(Delta l_C)/(Delta l_S) = (Y_S)/(Y_C)`
or `Delta l_C = Delta l_S xx (Y_S)/(Y_C) = Delta l_S xx (20 xx 10^11)/(12 xx 10^11) = 5/3 Delta l_S`
Also `Delta l_S + Delta l_C = 1 cm `(given)
` therefore Delta l_S + 5/3 Detla l_S = 1 ` or ` Delta l_S = 3/8 cm`
` therefore Deltal_C = 1 - Delta l_S = 1 - 3/8 = 5/8 cm`
so , the steel wire is elongated by `3/8 cm` and the copper is elongated by ` 5/8`cm
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