A string of length L and force constant k is stretched to obtain extension l. It is further stretched to obtainextension l1. The work done in second stretching is [MHT CET 2014]

# A string of length L and force constant k is stretched to obtain extension l. It is further stretched to obtainextension l1. The work done in second stretching is [MHT CET 2014]

1. A

$\frac{1}{2}k{l}_{1}\left(2l+{l}_{1}\right)$

2. B

$\frac{1}{2}k{l}_{1}^{2}$

3. C

$\frac{1}{2}k\left({l}^{2}+{l}_{1}^{2}\right)$

4. D

$\frac{1}{2}k\left({l}_{1}^{2}-{l}^{2}\right)$

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### Solution:

Work done in stretching a string to obtain an extension I,

${W}_{1}=\frac{1}{2}k{l}^{2}$

Similarly, work done is stretching a string to obtain extension

Now, work done in second stretching,

${W}_{2}={W}_{2}^{\text{'}}-{W}_{1}=\frac{1}{2}k{\left({l}_{1}+l\right)}^{2}-\frac{1}{2}k{l}^{2}=\frac{1}{2}k{l}_{1}\left(2l+{l}_{1}\right)$

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