A string of length L and force constant k is stretched to obtain extension l. It is further stretched to obtain extension `l_(1)`. The work done in second streching is

Options

A. `(1)/(2)kl_(1)(2l+l_(1))`
B. `(1)/(2)kl_(1)^(2)`
C. `(1)/(2)k(l^(2)+l_(1)^(2))`
D. `(1)/(2)k(l_(1)^(2)-l^(2))`

Answer

A

Explanation

(a) Work done in stretching a string to obtain an extension l is
`W_(1)=(1)/(2)kl^(2)`
Similarly, work done is stretching a string to obtain extension`(l+l_(1))`
`W'_(2)=(1)/(2)k(l_(1)+l)^(2)`
`W_(2)=W'_(2)-W_(1)=(1)/(2)k(l_(1)+l)^(2)-(1)/(2)kl^(2)=(1)/(2)kl_(1)(2l+l_(1))`