Question

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

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

Answer 1

The correct option is A $\pm 0.2c{m}^2$

Length of the rectangular plate is $L=10.0cm\pm 0.1cm$

Width of the plate $B=1.00cm\pm 0.01cm$

So, error in length $\Delta L=0.1cm$

Error in width $\Delta B=0.01cm$

Area of the plate $A=L\times B=10\times 1=10c{m}^2$

Maximum error in area $\Delta A=\pm (\frac{\Delta L}{L}+\frac{\Delta B}{B})\times A$

$⟹$ $\Delta A=\pm (\frac{0.1}{10}+\frac{0.01}{1})\times 10=\pm 0.2c{m}^2$