The length of a metallic sheet is measured as 10.0 cm using a metre scale of L.C. 0.1cm and its breadth is measured as 1.00 cm using a vernier callipers of L.C. 0.01cm, the error in area is

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$\pm 0 .2 {cm}^{2}$

$\pm 0.1 {cm}^{2}$

$\pm 0 .11 {cm}^{2}$

$\pm 0 .01 {cm}^{2}$

answer is D.

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Detailed Solution

$\begin{array}{l} A = lb; \frac{ΔA}{A} = \frac{Δl}{1} + \frac{Δb}{b} \\ \Rightarrow ΔA = A [\frac{Δl}{1} + \frac{Δb}{b}] \\ = 10 [\frac{0.1}{10} + \frac{0.01}{1}] = 10 [0.01 + 0.01] \\ = 10 [0.02] = 0.2 {cm}^{2} \end{array}$

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