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

Answer

A

Explanation

Here,` F= ax+bx^(2)`
`Dw=F dx, W=int_(0)^(L)F dx=int_(0)^(L)( ax+ bx^(2))dx`
`=[(ax^(2))/(2)+(bx^(3))/( 3)]_(0)^(L)=((aL^(2))/( 2)+(bL^(3))/( 3))`