Question

A physical quantity Q is given by (in picture)
The percentage error is A,B,C and D are 1%, 2% ,4% and 2% respectively.
find the percentage error of Q.

Answer 1

Here is your ans.

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Answer 2

Answer:

The percentage error of Q is 22%.

Explanation:

Given that,

$Q=\dfrac{A^2B^{\frac{3}{2}}}{C^4 D^{\frac{1}{2}}}$

The percentage error is

A = 1 %

B= 2%

C =4%

D =2%

We need to calculate the percentage error of Q

$\dfrac{\Delta Q}{Q}=2\dfrac{\Delta A}{A}+\dfrac{3}{2}\times\dfrac{\Delta B}{B}+4\dfrac{\Delta C}{C}+\dfrac{1}{2}\dfrac{\Delta D}{D}$

$\dfrac{\Delta Q}{Q}\times100=2\times\dfrac{\Delta A}{A}\times100+\dfrac{3}{2}\times\dfrac{\Delta B}{B}\times100+4\dfrac{\Delta C}{C}\times100+\dfrac{1}{2}\times\dfrac{\Delta D}{D}\times100$

$\dfrac{\Delta Q}{Q}\times100=2\times1\%+\dfrac{3}{2}\times2\%+4\times4\%+\dfrac{1}{2}\times2\%$

$\dfrac{\Delta Q}{Q}\times100=2\%+3\%+16\%+1\%$

$\dfrac{\Delta Q}{Q}\times100=22\%$

Hence, The percentage error of Q is 22%.