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Question

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

[ Y=2×1011 N/m2 ]



A
5×106
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B
3×106
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C
7×106
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D
8×106
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Solution

The correct option is B 3×106

From F.B.D of block in accelerating frame of elevator,

Fpseudo=ma0

Tension in the wire,
T=m(g+a0)=10(10+2)=120 N
So, stress in the wire,
σ=TA=1202×104
σ=6×105 N/m2
From Hooke's law, strain in the wire,
ϵ=σY
ϵ=6×1052×1011=3×106.


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