Question

9A square plate of side 10 cm is made of a metal of linear expansivity
210−5/K. As the plate is heated from 30oC to 100o, the area of one face
of the plate will increase to -------------

Answer 1

Condition:

A square plate of side $10\mathrm{cm}$ is made of a metal of linear expansivity $210 - 5 / \mathrm{K}$. As the plate is heated from $30\mathrm{oC}$ to $100\mathrm{o}$, the area of one face of the plate will increase to

Solution:

Let $10\, \text{cm} = l; 30{}^{\circ} = t_{1}; 100{}^{\circ} = t_{2}; 2 \times 10^{-5} K^{-1} = \alpha$.

We need to find $S$.

We used the formula: $S = l_{T}^{2}$.

$$l_{T} = l \left(1 + \alpha (t_{2} - t_{1})\right), \text{ so } S = \left(l \left(1 + \alpha (t_{2} - t_{1})\right)\right)^{2} \rightarrow S = \left(10 \left(1 + 2 \times 10^{-5} (100 - 30)\right)\right)^{2}.$$ $$S = 100.28\, \text{cm}^{2}.$$

Answer: $S = 100.28\, \text{cm}^2$.