A rubber of volume 2000 cc is alternately subjected to tension and released. The figure shows the stress-strain curve of rubber. Each curve is a quadrant of an ellipse. The amount of energy lost as heat per cycle per unit volume will be
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a
(π2-1)×16×102 J
b
(π4-1)×8×102 J
c
(π4-1)×32×102 J
d
(π2-1)×32×102 J
answer is D.
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Detailed Solution
Hysteresis loss corresponding to elasticity per unit volume of a substance is given by the area of hysteresis loop, i.e., stress-strain curve coresponding to one complete loading and deloading.Area of an ellipse = π x semi-majoraxis x semi-minor axisA1 = 14(π×8×4×102) and A2 = 14(π×8×4×102)Also, A3 = 8×4×102Area by hysteresis loop is A = A1+A2-A3A = 2[π4×8×4×102]-[8×4×102] = work done per cycle = energy lost per cycle per unit volume
A rubber of volume 2000 cc is alternately subjected to tension and released. The figure shows the stress-strain curve of rubber. Each curve is a quadrant of an ellipse. The amount of energy lost as heat per cycle per unit volume will be