First slide

Dimensions of physical quantities

Question

A physical quantity P is described by the relation $P = a^{1 / 2} b^{2} c^{3} d^{- 4}$ . If the relative errors in the measurement of a, b, c and d respectively, are 2%,1%, 3% and 5%, then the percentage error in P will be_______ %

Moderate

Solution

Here, $P = a^{1 / 2} b^{2} c^{3} d^{- 4}$
$\frac{ΔP}{P} = \frac{1}{2} \frac{Δa}{a} + 2 \frac{Δb}{b} + 3 \frac{Δc}{c} + 4 \frac{Δd}{d}$
or $(\frac{ΔP}{P} \times 100) % = (\frac{1}{2} \frac{Δa}{a} + 2 \frac{Δb}{b} + 3 \frac{Δc}{c} + 4 \frac{Δd}{d}) \times 100 %$
$\Rightarrow$ Percentage error in P
$= (\frac{1}{2} \times 2 + 2 \times 1 + 3 \times 3 + 4 \times 5) \times 100 = 32 %$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App