Question

A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation a = $b ^ { \alpha } c ^ { \beta } / d ^ { \gamma } e ^ { \delta }$ . If the maximum errors in the measurement of b, c, d and e are $b _ { 1 }$ %, $c _ { 1 }$ %, $d _ { 1 }$ % and $e _ { 1 }$ %, then the maximum error in the value of a determined by the experiment is

• A. (a) ($b _ { 1 } + c _ { 1 } + d _ { 1 } + e _ { 1 }$)%
• A. (b) ( $b _ { 1 } + c _ { 1 } - d _ { 1 } - e _ { 1 }$ )%
• A. (c) ( $\alpha b _ { 1 } + \beta c _ { 1 } - \gamma d _ { 1 } - \delta e _ { 1 }$ )%
• A. (d) ( $\alpha b _ { 1 } + \beta c _ { 1 } + \gamma d _ { 1 } + \delta e _ { 1 }$ )%

Answer 1

(d)

Sol. $a = b ^ { \alpha } c ^ { \beta } / d ^ { \gamma } e ^ { \delta }$

So maximum error in a is given by

$\left( \frac { \Delta a } { a } \times 100 \right) _ { \max } = \alpha \cdot \frac { \Delta b } { b } \times 100 + \beta \cdot \frac { \Delta c } { c } \times 100$

$+ \gamma \cdot \frac { \Delta d } { d } \times 100 + \delta \cdot \frac { \Delta e } { e } \times 100$

$= \left( \alpha b _ { 1 } + \beta c _ { 1 } + \gamma d _ { 1 } + \delta e _ { 1 } \right) \%$