A rubber of volume 2000 cc is alternately subjected to tension and released. The figure shown 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. `((pi)/(2)-1)xx16xx10^2J`
B. `((pi)/(4)-1)xx8xx10^2J`
C. `((pi)/(4)-1)xx32xx10^2J`
D. `((pi)/(2)-1)xx32xx10^2J`

Answer

D

Explanation

Hysteresis 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`=pixx`semi-major axis`xx`semi-minor axis
`A_1=(1)/(4)(pixx8xx4xx10^2)` and `A_2=(1)/(4)(pixx8xx4xx10^2)`
Also, `A_3=8xx4xx10^2`
Area of hysteresis loop is `A=A_1+A_2+A_3`
`A=2[(pi)/(4)xx8xx4xx10^2]-[8xx4xx10^2]`
`=`work done per cycle
`=`energy lost per cycle per unit volume.