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Question

One end of a steel wire is fixed to the ceiling of a moving elevator. A load of 20 kg hangs from the other end. If the elevator is moving up with an acceleration 1 m/s2 and Area of cross- section of wire is 2 cm2 then find the longitudnal strain in the wire.
[Take g=10 ms2,Y=2×1011 Nm2 ]

A
5.5×104
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B
5.5×106
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C
3×106
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D
2×104
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Solution

The correct option is B 5.5×106

FBD of block from the frame of reference of elevator
T=mg+ma=m(g+a)
From the data given in the question ,
T=20(10+1)=220 N
From the definition of modulus of elasticity, we know that
Y=F×lA×ΔlT×lA×Δl
Longitudinal Strain Δll=TAY2202×104×2×10115.5×106
Thus, option (b) is the correct answer.

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