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  • Solve this problem 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 :

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 :

  • Option 1)

    aL^{2}+bL^{3}

  • Option 2)

    \frac{1}{2}(aL^{2}+bL^{3})

  • Option 3)

    \frac{aL^{2}}{2}+\frac{bL^{3}}{3}

  • Option 4)

    \frac{1}{2}\left ( \frac{aL^{2}}{2}+\frac{bL^{3}}{3} \right )

 

Answers (2)

best_answer

As we have learned

Definition of work done by variable force -

W=\int \vec{F}\cdot \vec{ds}

- wherein

\vec{F} is variable force and \vec{ds} is small displacement

 

 At x = x 

F = ax + bx^2

WOrk done in displacing rubber through dx = Fdx 

W = \int_{0}^{L}(ax + bx^2)dx

= a \int_{0}^{L}xdx + b \int_{0}^{L }^2 dx

w = \frac {aL^2}{2} + \frac {bL^3}{3}

 

 

 

 

 


Option 1)

aL^{2}+bL^{3}

Option 2)

\frac{1}{2}(aL^{2}+bL^{3})

Option 3)

\frac{aL^{2}}{2}+\frac{bL^{3}}{3}

Option 4)

\frac{1}{2}\left ( \frac{aL^{2}}{2}+\frac{bL^{3}}{3} \right )

Posted by

SudhirSol

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