A string of length 'L' and force constant 'K' is stretched to obtain extension `'l'`. It is further stretched to obtain extension `'l'` . The work done in second stretching is

Options

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

Answer

A

Explanation

P.E. stored in the spring when it is stretched by a length l is `U_(1) = (1)/(2)Kl^(2)`
When it is stretched by a further distance `l_(1)`,
the P.E. `= (1)/(2) K(l + l_(1))^(2)`
`:.` Work done `= U_(2) - U_(1)`
`= (1)/(2) K[(l + l_(1))^(2) - l^(2)]`
`= (1)/(2)K [l^(2) + l_(1)^(2) + 2l l_(1) - l^(2)]`
`W = (1)/(2)Kl_(1) (2l + l_(1))`