Gravitation Question 216

Question: A rubber of volume 2000 cc is alternately subjected to tension and released. The 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

Options:

A)[(π21)×16×102J]

B) [(π41)×8×102J]

C)[(π41)×32×102J]

D)[(π21)×32×102J]

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Answer:

Correct Answer: D

Solution:

  • Hystersis loss corresponding to elasticity per unit volume of a substance is given by the area of hysteresis loop, i.e., stress-strain curve corresponding to one complete loading and deloading. Area of an ellipse = [π×] semi-major axis x semi-minor axis

    [A1=14(π×8×4×102)] And[A2=14(π×8×4×102)]

    Also, [A3=8×4×102] Area of hysteresis loop is [A=A1+A2A3]

    [A=2[π4×8×4×102][8×4×102]]

    [=[π21]×32×102J] = work done per cycle = energy lost per cycle per unit volume



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