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Q.

A person measures two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report correct value for AB as

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a

1.4 m ± 0.4 m

b

1.41 m ± 0.15 m

c

1.4 m + 0.3 m

d

1.4 m ± 0.2 m

answer is D.

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Detailed Solution

Given, A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 mLet, Y = AB  = (1.0)(2.0)   =  1.414 m∆YY = 12[∆AA+∆BB]= 12[0.21.0+0.22.0]  =  0.62×2.0⇒∆Y = 0.6 Y2×2.0 = 0.6×1.42×2.0 = 0.21Rounding off to one significant digit∆Y = 0.2 mThus, correct value forAB  = r+∆r = 1.4 ± 0.2 m
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