Two straight thin bars, one of brass and the other of steel are joined togethre side by side by short steel cross-pieces at `0^(@)C`, one cm long the centre lines of the bars being one cm apart. When heated to `100^(@)C`, the composite bar becomes bent into the arc of a circle. calculate the radius of this circle.
`alpha` for brass `=19xx10^(-6)` per `.^(@)C`
and `alpha` for steel `=11xx10^(-6)` per `.^(@)C`

Explanation

To solve the problem, we need to calculate the radius of curvature of the composite bar made of brass and steel when heated from \(0^\circ C\) to \(100^\circ C\).

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Coefficient of linear expansion for brass, \(\alpha_{brass} = 19 \times 10^{-6} \, \text{per } ^\circ C\)
- Coefficient of linear expansion for steel, \(\alpha_{steel} = 11 \times 10^{-6} \, \text{per } ^\circ C\)
- Original length of each bar, \(L = 1 \, \text{cm} = 0.01 \, \text{m}\)
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