Question

The length of a rectangular plate is measured by a meter scale and is found to be $10.0\text{cm}$ . Its width is measured by vernier callipers as $1.00\text{cm}$ . The least count of the meter scale and vernier callipers are $0.1\text{cm}\text{and}0.01\text{cm}$ respectively. Maximum permissible error in area measurement is

• A. Zero
• B. $\pm 0.1{\text{cm}}^2$
• C. $\pm 0.3{\text{cm}}^2$
• D. $\pm 0.2{\text{cm}}^2$

Answer 1

The correct option is D $\pm 0.2{\text{cm}}^2$

We know that, $A=l\times b$

$\therefore {\left(\frac{\Delta A}{A}\right)}_{max}=\frac{\Delta l}{l}+\frac{\Delta b}{b}=\frac{0.1}{10}+\frac{0.01}{1.00}=0.02$

$\Rightarrow (\Delta A{)}_{max}=\pm 0.02A$

$=\pm 0.02\times 10\times 1.00=\pm 0.2{\text{cm}}^2$