Question

A physical quantity X is connected from X = ab2/C. Calculate percentage error in X, when percentage error in a,b,c are 4,2 and 3 respectively.

Answer 1

Answer:

9.5%

Explanation:

Missing information :

In this question there is incorrect question .The correct question is

$x\ =\frac{ab^{2} }{\sqrt{c} }$

Given :

$x\ =\ \frac{ab^{2} }{\sqrt{c} }$

From the propagation of error property

$\Delta x = \Delta a + 2 \Delta b + 1 \Delta c\\\ \ \ x = \ \ a + \ \ \ \ b + \ \ \ \ c$----------------------Eq(1)

Putting the respective value 4,2 and 3 in the Eq(1) we get

This gives

$percentage \ error \ = 4\ +\ 2*2\ +\ \frac{3}{2}\\ percentage \ error \ = 4+4+\frac{3}{2} \\percentage \ error \ = 8+\frac{3}{2}\\ percentage \ error \ = 8+1.5\\percentage \ error \ = 9.5\\Therefore \ 9.5\%$