Question

A physical quantity is given by - X = p2q3/2÷r4s1/2 the percentage error in p ,q,r,and s are 1%,2%,4%,and 2% calculate the percentage error in X

Answer 1

Answer:

% in X =2*1+(3/2)*2+4*4+(1/2)*2

Answer 2

Given that,

A physical quantity is given by :

$X=\dfrac{p^2q^{3/2}}{r^4s^{1/2}}$

The percentage error in p, q, r and s are 1 %,2 %,4 %,and 2 %.  

To find,

We need to find the percentage error in X.

Solution,

The percentage error in X is given by :

$\dfrac{\Delta X}{X}=2\times \dfrac{\Delta p}{p}+\dfrac{3}{2}\times \dfrac{\Delta q}{q}+4\times \dfrac{\Delta r}{r}+\dfrac{1}{2}\times \dfrac{\Delta s}{s}$

Putting the percentage error in p, q, r and s are as 1 %,2 %,4 %,and 2 %

$\dfrac{\Delta X}{X}=2\times 1+\dfrac{3}{2}\times 2+4\times 4+\dfrac{1}{2}\times 2\\\\\dfrac{\Delta X}{X}=22\%$

So, the percentage error in X is 22 %.

Learn more,

Percentage error

https://brainly.in/question/10536255