Question

A physical quantity X is related to four measurable quantities a, b, c and d as follows X = a²b³c⁵/d^-2. The percentage error in the measurement of a, b, c and d are 1%, 2%, 2% and 4% respectively. What is the percentage error in quantity X?

• A. (a) 15%
• A. (b) 17%
• A. (c) 21%
• A. (d) 23%

Answer 1

(c)

Sol. As $X = a ^ { 2 } b ^ { 3 } c ^ { 5 / 2 } d ^ { - 2 }$

The percentage error in X is

$\frac { \Delta \mathrm { X } } { \mathrm { X } } \times 100 = \left[ 2 \left( \frac { \Delta \mathrm { a } } { \mathrm { a } } \right) + 3 \left( \frac { \Delta \mathrm { b } } { \mathrm { b } } \right) + \frac { 5 } { 2 } \left( \frac { \Delta \mathrm { c } } { \mathrm { c } } \right) + 2 \left( \frac { \Delta \mathrm { d } } { \mathrm { d } } \right) \right] \times 100$ $= 2 \times 1 \% + 3 \times 2 \% + \frac { 5 } { 2 } \times 2 \% + 2 \times 4 \% = 21 \%$