A wire of area of cross-section 3.0mm2 and natural length 50 cm is fixed at one end and a mass of 2.1 kg is hung from the other end. Young's modulus of the material of wire is 1.9 x 1011 N / m2 . Take g =10m / s2. The potential energy stored in the wire in steady state will be
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a
1⋅9×10−5J
b
1⋅9×10−4J
c
9⋅1×10−4J
d
9⋅1×10−5J
answer is B.
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Detailed Solution
Tension in the wire T =mg=(2.1)(10) = 21 newtonStress = T / A = 21N / 3.0 mm2=7⋅0×106N/m2Strain =Stress / Y =3.7 x 10-5Volume of wireV= (3 .00 mm2) (5o cm)=3⋅0×10−6m2×0⋅50m=1⋅5×10−6m3U=12× stress × strain × volume =1⋅9×10−4J