Question

The length of a strip measured with a meter rod is 10.0 cm its width measured with a vernier caliper is 1.00 cm. The least count of the meter rod is 0.1 cm and that of vernier caliper caliper 0.01 cm water will be error in its area?

• A. $\pm 13$%
• B. $\pm 7$%
• C. $\pm 4$%
• D. $\pm 2$%

Answer 1

The correct option is D $\pm 2$%

Given,

Least count of tape is $0.1cm$

Least count of Vernier caliper is $0.01cm$

Length, $L=10cm$

Width, $W=1cm$

$area$,$A=Length\times width=L\times W$

Take ln and differentiate,

$\frac{\Delta A}{A}=\frac{\Delta L}{L}+\frac{\Delta W}{W}$

$\frac{\Delta A}{A}=\frac{0.1}{10}+\frac{0.01}{1}=0.02=2percent$

Hence, error in area is $\pm 2$ %