A work of `2 times 10^(-2)J` is done on a wire of length 50 cm and area of cross-section 0.5 `mm^(2)`. If the Young's modulus of the material of the wire is `2 times 10^(10)Nm^(-2)`, then the wire must be :

Options

A. elongated to 50.1414 cm
B. contracted by 2.0 mm
C. stretched by 0.707 mm
D. of length changed to 50.2 cm

Answer

C

Explanation

The work done by wire is stored as potential energy in the wire
`" "U=1/2 times "Young.s modulus" times ("strain")^(2)`
Given, `" "Y=2 times 10^(10)Nm^(-2)`,
Strain `=1/L=l/(50 times 10^(-2)), U=2 times 10^(-2)J`
`therefore 2 times 10^(-2)=1/2 times 2 times 10^(10) times (l/(50 times 10^(-2)))^(2)`
`rArr" "l approx 0.707` mm (stretched)