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) + bL^(2)`
B. ` (1)/(2)(aL^(2) + bL^(3) )`
C. `(aL^(2))/(2) + (aL^(3))/(3)`
D. `(1)/(2) (9aL^(2))/(2) + (bL^(3))/(3)))`

Answer

C

Explanation

(c ) Work done in stretching the rubber - band by a distance `dx` is
` dW = F dx = (ax + bx^(2) )dx`
Integrating both sides ,
`W = int_(0)^(L) axdx + int _(0)^(L) dx^(2) dx = (aL^(2))/(2) + (bL^(3))/(3)`