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The error in the measurement of the length and the breadth of a rectangular table is 1%. If the length and breadth of the table are 1 m and 50 cm respectively, then the area of the table including error is

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a

$(0.5 \pm 0.1) m^{2}$

b

$(0.5 \pm 0.01) m^{2}$

c

$(5000 \pm 10) c m^{2}$

d

$(5000 \pm 1) c m^{2}$

answer is B.

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Detailed Solution

$A = l \times b = 1 \times \frac{50 cm}{100} = 0.5 m^{2} \frac{ΔA}{A} = \frac{Δl}{l} + \frac{Δb}{b} ΔA = 0.5 \times (\frac{Δl}{l} \times \frac{100}{100} + \frac{Δb}{b} \times \frac{100}{100}) ΔA = 0.5 \times (\frac{1}{100} + \frac{1}{100}) = \frac{0.5}{50} m^{2} ΔA = 0.01 m^{2} \Rightarrow A = (0.5 \pm 0.01) m^{2}$

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