Question

A physical quantity Q is calculated using the formula $Q=\frac{1}{10}\left[\frac{x{y}^2}{z^{1/3}}\right]$, where x, y and z are experimentally measured quantities. If the fractional error in the measurement of x, y and z are 2%, 1% and 3% respectively then the fractional error in Q is a%. Find a.

• A. 5.55
• B. 5.42
• C. 5.32
• D. 5

Answer 1

Answer: (D)

5

$\left[\frac{\Delta Q}{Q}\right]\times 100=[\frac{\Delta x}{x}+\frac{2\Delta y}{y}+\frac{1}{3}\frac{\Delta z}{z}]\times 100$

$=[2+2\times 1+\frac{1}{3}\times 3]$

$=5$