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

D

Explanation

Work done in stretching a string to obtain an extension l is
`W_(1) = (1)/(2) Kl`
Similarly , work done is stretching a string to obtain extension `l_(1)` is
`W_(2) = (1)/(2) kl_(1)^(2)`
`therefore` Work done is second case
`= W_(2) - W_(1) = (1)/(2) K(l_(1)^(2) - l^(2))`