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. `1/2kt_1(2t+t_1)`
B. `1/2Kt_(1)^(2)`
C. `1/2K(t^2-t_(1)^2`
D. `1/2K(t_(1)^(2)-t^(2))`

Answer

D

Explanation

Work done in stretching a string to obtain an extension I is
`w_1=1/2Kt^2`
Similarly, work done in stretching a string to obtain extension `t_1` is
`w_2=1/2kt_1^2`
`therefore` Work done in second stretching will be
w=`w_2-w_1`
=`1/2K(t_1^2-t^2)`