A wire of natural length l, young's modulus Y and ares of cross-section A is extended by x. Then, the energy stored in the wire is given by

Options

A. `(1)/(2) (YA)/(l) x^(2)`
B. `(1)/(2) (Yl)/(A) x^(2)`
C. `(1)/(2) (YA)/(l^(2)) x^(2)`
D. `(1)/(2) (A)/(Yl) x^(2)`

Answer

A

Explanation

Energy stored in the wire is `U= (1)/(2) xx` stress `xx` strain `xx` volume
`=(1)/(2) xx Y xx ("strain")^(2) xx Al " " ( :. Y= ("stress")/("strain"))`
`= (1)/(2) xx Y xx ((x)/(l))^(2) xx Al = (1)/(20 (YAx^(2))/(l)`