A metal wire of length L, area of cross-section A and young's modulus `Y` is stretched by a variable force `F` such that `F` is always slightly greater than the elastic forces of resistance in the wire. When the elongation of the wire is `l`

Options

A. the work done by `F` is `(YAl^(2))/(2L)`
B. the work done by `F` is `(YAl^(2))/(L)`
C. the elastic potential energy stored in the wire is `(Yal^(2))/(2L)`
D. the elastic potential energy stored in the wire is ` (Yal^(2))/(4L)`

Answer

A, C

Explanation

` W_(F) `= elastic potential energy stored in the wire
` = 1/2 k (Deltal)^(2)`
` = 1/2((YA)/(L))(l)^(2) = (YAl^(2))/(2L)`