Question

A physical quantity ' $y$ ' is represented by the formula $y=m^{2} r^{-4} g^{x} l^{-\frac{3}{2}}$ If the percentage errors found in $y, m, r, l$ and $g$ are $18,1,0.5,4$ and $p$ respectively, then find the value of $x$ and

• A. $5$ and $\pm 2$
• B. $4$ and $\pm 3$
• C. $\frac{16}{3}$ and $\pm \frac{3}{2}$
• D. $8$ and $\pm 2$

Answer 1

Answer: (C)

$\frac{\Delta y}{y}=\frac{2 \Delta m}{m}+\frac{4 \Delta r}{r}+\frac{x \Delta g}{g}+\frac{3}{2} \frac{\Delta l}{l} $
$18=2(1)+4(0.5)+x p+\frac{3}{2}(4)$
$8=x p$
By checking from options.
$x=\frac{16}{3}, p=\pm \frac{3}{2}$