Ncert Exercises & Solutions

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

1.	will also double.	2.	will become four times.
3.	will remain the same.	4.	will decrease.

(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)

$L_{t} = L_{o} (1 + α ∆ T)$

where

∆

$∆$ T is the change in the temperature,

L_{0}

$L_{0}$ is the original length,

α

$α$ is the coefficient of linear expansion and

L_{t}

$L_{t}$ is the length at temperature T.

Now, we can write,

∆ L = L_{t} - L_{o} = L_{o} α ∆ T

$∆ L = L_{t} - L_{o} = L_{o} α ∆ T$

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}

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

Y \propto \frac{1}{∆ T}

$Y \propto \frac{1}{∆ T}$ , when temperature increases, Y decreases.