Question

A metal washer has a hole of diameter $d_1$ and an external diameter $d_2$, where $d_2=3d_1$. On heating ,$d_2$ increases by $0.3\%$. Then $d_1$ will increase or decrease by what percentage

• A. decrease by $0.1$
• B. decrease by $0.3$
• C. increase by $0.1$
• D. increase by $0.3$

Answer 1

The correct option is D increase by $0.3$

Increase in length of in the inner diameter $d_i$ is

$\Delta d_i=d_i\times \alpha \times \Delta T$

Percentage increase in length of inner diameter $d_i$ is

$\frac{\Delta d_i}{d_i}\times 100=\alpha \times \Delta T\times 100$ .....$\left(1\right)$

Increase in length of in the outer diameter $d_o$ is

$\Delta d_0=d_0\times \alpha \times \Delta T$

Percentage increase in length of outer diameter $d_o$ is

$\frac{\Delta d_0}{d_0}\times 100=\alpha \times \Delta \times 100$ .....$\left(2\right)$

so percentage increase in inner and outer diameter is same and is equal to $0.3\%$