We would like to increase the length of a 15 cm long copper rod of cross section `4mm^2` by 1 mm. The energy absorbed by the rod if it is heated is `E_1`. The energy absorbed by the rod if it is stretched slowly is `E_2`. Then find `E_1//E_2`. [Various parameters of copper are density `=9xx10^3 Kg//m^(3)`, thermal coefficient of linear expansion `=16xx10^-6//K`, Young's modulus `=135xx190Pa`, specific heat `= 400 J//kg-K`]

Explanation

To solve the problem, we need to find the ratio \( \frac{E_1}{E_2} \), where \( E_1 \) is the energy absorbed by the copper rod when heated, and \( E_2 \) is the energy absorbed when the rod is stretched slowly.

### Step 1: Calculate \( E_1 \)

The energy absorbed by the rod when heated can be expressed using the formula:
\[ E_1 = m \cdot S \cdot \Delta T \]
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