Question

A physical quantity is given by $X = M^aL^bT^c$. The percentage error in measurement of M, L and T are $\alpha$, $β$ and $\gamma$ respectively. Then, the maximum % error in the quantity X is

• A. $a\alpha + bβ + c\gamma$
• B. $a\alpha + bβ - c\gamma$
• C. $\frac{a}{\alpha} +\frac{b}{\beta}+\frac{c}{\gamma}$
• D. none of these.

Answer 1

Answer: (A)

$X = M^aL^bT^c$
Percentage error in X
$\frac{\Delta X}{X} \times 100 = a \frac{\Delta M}{M} \times 100 +b \frac{\Delta L}{L} \times 100 +c \frac{\Delta T}{T}\times 100$ As given,
$\frac{\Delta M}{M} \times 100 = \alpha, \,\frac{\Delta L}{L} \times 100 = \beta, \,\frac{\Delta T}{T}\times 100 = \gamma$
$\therefore \quad$ Percentage error in $X = a\alpha + bβ + c\gamma.$