When a rubber band is streched by a distance `x` , if exerts restoring force 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^2`
D. `1/2(aL^2 + bL^2)`

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 = int_0^LFdx = int_(0)^(L) (ax + bx^2) dx implies W = [a (x^2)/2 + b(x^3)/(3)] = (aL^2)/(2) + (bL^3)/(3)`