Question

A wire of length 'L' and area of cross-section · A' is made of material of Young's modulus 'Y'. It is stretched by an amount 'x'. The work done in stretching the wire is ______.

Options

• `("Y""x"^2"A")/"2L"`

• `(2"Y""x"^2"A")/"L"`

• `("Y""x""A")/"2L"`

• `("Y""x"^2"A")/2`

Answer 1

A wire of length 'L' and area of cross-section · A' is made of material of Young's modulus 'Y'. It is stretched by an amount 'x'. The work done in stretching the wire is `underline(("Y""x"^2"A")/"2L")`.

Explanation:

If a force Fis applied along the length L of wire for stretching by an amount x, then Young's modulus is given by

Y = `"stress"/"strain" = "FL"/"Ax"`

where, A = area of cross-sectional ⇒ F = `"YA"/"L"`x

The work done in stretching the wire is given by

W = `int_0^x "F" * "dx" = int_0^x "YA"/"L" x = "YA"/"L" [x^2/2]_0^x = ("YAx"^2)/"2L"`