Question

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

A) aL2/2 + bL3/3
B) (aL2 + bL3)/3
C) aL2 + bL3
D) (aL2/2 + bL3/3)/2

Answer 1

Answer: option A

Explanation: check the attached photo

Answer 2

Answer:

A

Explanation:

Restoring force : F = ax+bx²

we know that work done = ∫F.dx

here w = ∫(0 to L) (ax+bx²).dx

= [ax²/2+bx³/3] 0 to L (∵by integration)

∴ w = aL²/2+bL³/3

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