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Question

One end of a steel wire is fixed to the ceiling of an elevator moving up with an acceleration 2 m/s2 and a load of 10 kg hangs from other end. Area of cross -section of the wire is 2 cm2. The longitudinal strain in the wire is (g=10 m/s2 and Y=2×1011 Nm2)

A
4×106
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B
3×106
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C
8×106
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D
2×106
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Solution

The correct option is B 3×106
Given that, a load of 10 kg hangs in an elevator which is moving up with an acceleration 2 m/s2
Let a0=2 m/s2
So, tension in the steel wire is given by
T=m(g+a0)=10(10+2)=120 N
Stress in the wire =(TA)=1202×104=60×104 Nm2
and we know that,
Y=Logitudinal StressLongitudinal Strain
Longitudinal Strain=Longitudinal StressY
ΔLL=60×1042×1011
=30×107 or 3×106
Thus, option (b) is the correct answer.

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