When a rubber bandis streched by a distance `x` , if exerts resuring foprce of magnitube `F = ax + bx^(2)` where`a` and `b` are constant . The work in streached the unstreched rubber - band by `L` is

Options

A. `(aL^(2))/(2)+(bL^(3))/(3)`
B. `(1)/(2)((aL^(2))/(2)+(bL^(3))/(3))`
C. `(bL^(2))/(2)-(aL^(3))/(3)`
D. `(1)/(2)((bL^(2))/(2)-(aL^(3))/(3))`

Answer

A

Explanation

Restoring force on rubber-band,
`F = ax + bx^(2)`
Work done in stretching the rubber-band by a small amount `dx`.
`dW = Fdx`
Net work done in stretching the rubber-band by `L` is
`W = int dW = underset(0)overset(L) int Fdx = underset(0)overset(L) int (ax + bx^(2)) dx`
`rArr W =[a(x^(2))/(2) + b(x^(3))/(3)]_(0)^(L) = (aL^(2))/(2) + (bL^(2))/(3)`.