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Question

Two wires of different materials, each 2m long and of diameter 2mm, are joined in series to form a composite wire. What force will produce a total length of 0.9 mm. Given Young's modulus of both wires is (Y1=2×1011pa) and (Y2=6×1011 Pa)

A
282.6 N
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B
212 N
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C
319.8 N
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D
382.6 N
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Solution

The correct option is D 212 N

Given.

Length of both wires, L=2m

Radius of both wires, r=1mm=1×103m

Total extension of joined wire, ΔLnet=0.9mm=9×104m

Both wire join in series, so tension in both is equal

T=Y1AΔL1L=Y2AΔL2L

Net extension in joined wire.

ΔLnet=ΔL1+ΔL2=TLY1A+TLY2A=TLA(1Y1+1Y2)

ΔLnet=TLA(1Y1+1Y2)

T=AΔLnetL(1Y1+1Y2)=π(103)2×9×1042(12×1011+16×1011)=212.05 N

Total force produced in joined wire is 212 N


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