Question 106: Units , Dimensions and Error Analysis

Question

A physical quantity P is given as
$$P = {{{a^2}{b^3}} \over {c\sqrt d }}$$
The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be

Accepted Answer

The percentage error in a quantity that is a product or quotient of other quantities is given by the sum of the percentage errors in those quantities, each multiplied by the power to which it is raised in the expression for the quantity.
Given the physical quantity P as
$$P = \frac{a^2b^3}{c\sqrt{d}}$$
The percentage error in P, denoted as $\Delta P/P$, is given by:
$$\frac{\Delta P}{P} = 2 \left(\frac{\Delta a}{a}\right) + 3 \left(\frac{\Delta b}{b}\right) + \left(\frac{\Delta c}{c}\right) + \frac{1}{2} \left(\frac{\Delta d}{d}\right)$$
Substituting the given percentage errors for a, b, c, and d:
$$\frac{\Delta P}{P} = 2(0.01) + 3(0.02) + 0.03 + \frac{1}{2}(0.04) = 0.02 + 0.06 + 0.03 + 0.02 = 0.13$$
Therefore, the percentage error in P is 13%.

Answer

12%

Answer

13%

Answer

16%

Answer

14%

Units , Dimensions and Error Analysis

A physical quantity P is given as $P = {{{a^2}{b^3}} \over {c\sqrt d }}$ The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4% respectively. The percentage error in the measurement of quantity P will be

Choose the correct answer: