Question

The temperature of a wire is doubled. The Young’s modulus of elasticity

Answer 1

As Y ∝ 1/ ∆T

When temperature increases ∆T increases, hence Y decreases.

Answer 2

Explanation:

The property of a solid that measures its stiffness is called the young's modulus of elasticity. Mathematically, it can be written as :

$Y=\dfrac{F/A}{\Delta L/L}$............(1)

Where,

$F/A$ is normal stress

$\Delta L/L$ is the longitudinal strain

We know that the coefficient of linear expansion is given by :

$\alpha=\dfrac{\Delta L}{L_0\Delta T}$

$\Delta L=\alpha L_0\Delta T$...........(2)

Where,

L₀= original length

$\Delta L$ is change in length.

From equation (1) and (2)

$Y\propto\dfrac{1}{\Delta T}$

So, from the above relation the young's modulus is inversely proportional to the temperature. When the temperature of the wire is doubled, then the young's modulus of elasticity becomes half.