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)K l_(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

Potential energy stored by the string to stretch is `'l'` is
` u_(1)=(1)/(2) Kl^(2) " " ` ….(i)
Potential energy stored by the string when it is further extened by `l_(1)` is,
`u_(2)=(1)/(2) K(l+l_(1))^(2)`
`therefore ` Work done is secent stretching is,
`u_(2)-u_(1)=(1)/(2) K(l+l_(1))^(2)-(1)/(2) K(l^(2))`
`=(1)/(2) K[l^(2)+2l l_(1)+l_(1)^(2) -l^(2)]`
`=(1)/(2) K(l_(1)^(2) +2l l_(1))`
`=(1)/(2) K l_(1)(l_(1) +2l)`