SATHEE: Work Energy And Power Question 146

Work Energy And Power Question 146

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

Options:

A) $\frac{a L^{2}}{2} + \frac{b L^{3}}{3}$

B) $\frac{1}{2} (\frac{a L^{2}}{2} + \frac{b L^{3}}{3})$

C) $a L^{2} + b L^{3}$

D) $\frac{1}{2} (a L^{2} + a L^{3})$

Show Answer

Answer:

Correct Answer: A

Solution:

[a] Restoring force on rubber-band, $F = a x + b x^{2}$

Work done in stretching the rubber-band by a small amount $d x, d W = F d x$

Net work done in stretching the rubber-band by L is

$W = \int d W = \int_{0}^{L} F d x = \int_{0}^{L} (a x + b x^{2}) d x$

$\Rightarrow W = {[a \frac{x^{2}}{2} + b \frac{x^{3}}{3}]}_{0}^{L} = \frac{a L^{2}}{2} + \frac{b L^{3}}{3}$

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Work Energy And Power Question 146

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,

Options:

Answer:

Solution:

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