Question

A metal plate of area $1)2m^2$ increases its area by $2)4\times {10}^{-4}{m}^2$ when it is heated from $0^{\circ }C$ to ${100}^{\circ }C$. The coefficient of cubical expansion of the metal expressed in per ${}^{\circ }C$ is

• A. $2\times {10}^{-6}$
• B. $4\times {10}^{-6}$
• C. $6\times {10}^{-6}$
• D. $3\times {10}^{-6}$

Answer 1

The correct option is D $3\times {10}^{-6}$

Increase in area = initial area x coefficient of area expansion x change in temperature

Here all the values are given except coefficient of area expansion

Coefficient of areal expansion$=$increase in area/(initial area $\times$ change in temperature)

Coefficient of areal expansion $=\frac{2.4\times {10}^{-4}}{1.2\times 100}$
Putting the given values, we get coefficient of area expansion = 2 x 10${}^{-6}$
Now coefficient of volume expansion = $\frac{3}{2}$ x coefficient of area expansion =$3\times$ 10${}^{-6}$