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) KI_(1) (2I + I_(1))`
B. `(1)/(2) KI_(1)^(2)`
C. `(1)/(2) K (I^(2) + I_(1)^(2))`
D. `(1)/(2) (I_(1)^(2) - I^(2))`

Answer

d

Explanation

Work done in stretching a string to obtain in extension I is
`W_(1) = (1)/(2) Ki^(2)`
`:.` work done in second case `= W_(2) - W_(1) K (K_(1)^(2) - I^(2))`