Question

A physical quantity p is given as p=a3/√bc and percentage errors in the measurement of a

Answer 1

Answer:

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Answer 2

Answer:

a = $\frac{1}{3}\times [\frac{\Delta p}{p}\times 100 - \frac{1}{2}\times \frac{\Delta b}{b}\times 100 - \frac{1}{2}\times \frac{\Delta c}{c}\times 100]$

Step-by-step explanation:

According to this question

$p$ = $\frac{a^3}{\sqrt bc}$

We can find the percentage errors in the measurement of a

Now, $\frac{\Delta p}{p}$ = $3\frac{\Delta a}{a} + \frac{1}{2}\times \frac{\Delta b}{b} + \frac{1}{2}\times \frac{\Delta c}{c}$

$3\frac{\Delta a}{a}$ = $\frac{\Delta p}{p} - \frac{1}{2}\times \frac{\Delta b}{b} - \frac{1}{2}\times \frac{\Delta c}{c}$

$\frac{\Delta a}{a}$ = $\frac{1}{3}\times [\frac{\Delta p}{p} - \frac{1}{2}\times \frac{\Delta b}{b} - \frac{1}{2}\times \frac{\Delta c}{c}]$

Multiple both side with 100

$\frac{\Delta a}{a}\times 100$ = $\frac{1}{3}\times [\frac{\Delta p}{p}\times 100 - \frac{1}{2}\times \frac{\Delta b}{b}\times 100 - \frac{1}{2}\times \frac{\Delta c}{c}\times 100]$

Hense, percentage errors in the measurement of a = $\frac{1}{3}\times [\frac{\Delta p}{p}\times 100 - \frac{1}{2}\times \frac{\Delta b}{b}\times 100 - \frac{1}{2}\times \frac{\Delta c}{c}\times 100]$