A wire of length L and cross sectional area A is made of a material of Young's modulus Y. If the wire is streched by an amount x, the work done is………………

Options

A. `(Yax)/(2L)`
B. `(Yax^2)/(L)`
C. `(Yax^2)/(2L)`
D. `(2YAx^2)/(L)`

Answer

C

Explanation

Total energy `=(1)/(2)xx`stress`xx`strai n`xx`volume
`=(1)/(2)xxYxx(strai n)^2xx`volume
`=(1)/(2)Yxx(x^2)/(L^2)xxAL=(1)/(2)(YAx^2)/(L)`
Correct choice is (c ).