When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude `F = ax + bx^2` where a and b are constants. The work done in stretching the unstretched rubber band by L is :

Options

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

Answer

C

Explanation

`F = a +bx^(2)`
`dW =Fdx`
`W = int_(0)^(L) (ax+bx^(2))dx`
`W = (aL^(2))/2 + (bL^(3))/3 `