Question

A 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 -------------
1056cm2
1042cm2
1028cm2
1014cm2

Answer 1

Queston#21065

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

1056cm2

1042cm2

1028cm2

1014cm2

Solution:

Let:

$$L = 10 \text{ cm}$$ $$T_1 = 30{}^\circ \text{C}$$ $$T_2 = 100{}^\circ \text{C}$$ $$\alpha = 2 \times 10^{-5} \text{ K}^{-1}$$

S - ?

$$S = L_t^2$$ $$L_t = L(1 + \alpha(T_2 - T_1))$$ $$S = (L(1 + \alpha(T_2 - T_1))^2$$ $$S = (10(1 + 2 \times 10^{-5}(100 - 30))^2 = 100.28 \text{ cm}^2$$

Answer: 100.28 cm²