When a rubber-band is stretched by a distance x, it exerts 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 + bL³ (b) 1/2(aL² + bL³) (c) aL²/2 + bL³/3 (d) 1/2(aL²/2 + bL³/3)

Answer: (c). Work done against a variable force: W = ∫₀L F dx. W = ∫₀L (ax + bx²) dx = aL²/2 + bL³/3 So the answer is (c) aL²/2 + bL³/3.

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Work by a Variable Force

When a rubber-band is stretched by a distance $x$ , it exerts 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:

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Answer: (c)

Work done against a variable force: $W = \int_0^L F\,dx$ .
$W = \int_0^L (ax + bx^2)\,dx = \frac{aL^2}{2} + \frac{bL^3}{3}$
So the answer is (c) $\frac{aL^2}{2} + \frac{bL^3}{3}$ .

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