Question

A physical quantity $Q$ is found to depend on observables $x,y$ and $z$, obeying relation $Q=\frac{x^{2/5}{z}^3}{y}$. The percentage error in the measurements of $x,y$ and $z$ are $1\%$, $2\%$ and $4\%$ respectively. What is percentage error in the quantity $Q$ will be :

• A. $5\%$
• B. $4.5\%$
• C. $11\%$
• D. $7.75\%$

Answer 1

Answer: (C)

$11\%$

The given quantity $Q=\frac{x^3{y}^2}{z}$

Percentage error in Q $\frac{\Delta Q}{Q}\times 100=3\frac{\Delta x}{x}\times 100$ $+2\frac{\Delta y}{y}\times 100+\frac{\Delta z}{z}\times 100$

Percentage error in $x,y$ and $z$ are $1\%$, $2\%$ and $4\%$ respectively.

$⟹$ $\frac{\Delta Q}{Q}\times 100=3\left(1\right)+2\left(2\right)+1\left(4\right)=11$ %