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Standard XII

Physics

Distance Time Graph

A physical qu...

Question

A physical quantity $Z$ as a function of time is given as $Z (t) = A^{\frac{3}{2}} e^{- k t},$ where $k = 0.1 s^{- 1}$ . The measurement of A has an error of $2.00 % .$ If the error in the measurement of time is $1.25 %,$ then the percentage error in the value of $Z (t)$ at $t = 10 s$ would be

2.50 %

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3.50 %

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3.75 %

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4.25 %

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Solution

The correct option is D $4.25 %$
$l n Z = \frac{3}{2} l n A - k t$
$\frac{Δ Z}{Z} = \frac{3}{2} \frac{Δ A}{A} + k t \frac{Δ t}{t} = \frac{3}{2} \times 2 + 1.25 = 4.25 %$ .

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A physical quantity Z as a function of time is given as Z(t)=A32e–kt, where k=0.1 s–1. The measurement of A has an error of 2.00%. If the error in the measurement of time is 1.25%, then the percentage error in the value of Z(t) at t=10 s would be

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A physical quantity $Z$ as a function of time is given as $Z (t) = A^{\frac{3}{2}} e^{- k t},$ where $k = 0.1 s^{- 1}$ . The measurement of A has an error of $2.00 % .$ If the error in the measurement of time is $1.25 %,$ then the percentage error in the value of $Z (t)$ at $t = 10 s$ would be

The correct option is D $4.25 %$
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