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^(2)J`
B. `((pi)/(4)-1)xx8xx10^(2)J`
C. `((pi)/(4)-1)xx32xx10^(2)J`
D. `((pi)/(2)-1)xx32xx10^(2)J`

Answer

D

Explanation

Hysteris loss corresponding to elesticity per unit volume of a substance is given by the area of hysetersis loop, i.e., stress-strian curve corresponding to one complete loading and deloading

Area of an eliplse `= pi xx` semi major axis `xx` sremi-minor axis `A_(1) = (1)/(4) (pi xx 8xx4xx10^(2))` and `A_(2) = (1)/(4) (pi xx 8xx4xx10^(2))` Also, `A_(3) = 8xx4xx10^(2)`
Area of hystersis loop is `A = A_(1) + A_(2) - A_(3)`
`A = 2 [(pi)/(4)n xx 8xx4xx10^(2)] - [8xx4xx10^(2)]`
= woerk done per cylce
= energy lost per cycle per unti volume