Two wires are made of the same metal. The length of the first wire is half that of the second and its diameter is double that of the second wire. If equal loads are applied on both wires, find the ratio of increase in their lengths?
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L1 = l
L2= 2l
diameter= d1= 2d = 4r
d2= d = 2r
r1= 2r
r2 = r
the young modulus for both wires are same so
F1/ A1 divide ΔL1/ L1 = F2/ A2 divide ΔL2/ L2
as load is same so F1= F2
1/xr1² divide ΔL1/l = 1/xr2² divide ΔL2/ 2l
1/ ΔL1 x 4r² = 2/ ΔL2 x r²
ΔL1/ ΔL2 = 1/8
L2= 2l
diameter= d1= 2d = 4r
d2= d = 2r
r1= 2r
r2 = r
the young modulus for both wires are same so
F1/ A1 divide ΔL1/ L1 = F2/ A2 divide ΔL2/ L2
as load is same so F1= F2
1/xr1² divide ΔL1/l = 1/xr2² divide ΔL2/ 2l
1/ ΔL1 x 4r² = 2/ ΔL2 x r²
ΔL1/ ΔL2 = 1/8
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