Question

A rubber band stretched though a distance x exerts a restoring force of magnitude F = ax + bx² where a and b are constants. The work done in stretching the unstretched band by L is

(1) aL² + bL³

(2) 1/2 (aL² + bL³)

(3) 1/2 aL² + 1/3 bL³

(4) 1/2 (aL² + bL³/3)

Answer 1

(3) 1/2 aL² + 1/3 bL³

As the force is variable; the work done is calculated by 

integration. Initially x = 0  [Unstretched band] 

and finally x = L  [Given]

∴ Work done W = |dW| = ∫Fdx