Ncert Exercises & Solutions

The temperature of the wire is doubled. Young's modulus of elasticity:

(4) Hint: Young's modulus is the property of the material of the wire.

Step 1: Find the change in length of the wire.

We know that with an increase in temperature, the length of a wire changes as;

L_{t} = L_{o} (1 + α ∆ T)

where

∆

T is the change in the temperature,

L_{0}

is the original length,

α

is the coefficient of linear expansion and

L_{t}

is the length at temperature T.

Now, we can write,

∆ L = L_{t} - L_{o} = L_{o} α ∆ T

Step 2: Find Young's modulus.

Young's modulus (Y) =

\frac{Stress}{Strain} = \frac{F L_{o}}{A \times ∆ L} = \frac{{FL}_{o}}{{AL}_{o} α ∆ T} \propto \frac{1}{∆ T}

Y \propto \frac{1}{∆ T}

, when temperature increases, Y decreases.