Physics And Measurement Question 301
Question: A physical quantity Q is related to four observables x, y, z and t by the relation $ Q=\frac{{{x}^{2/5}}z^{3}}{y\sqrt{t}} $ The percentage errors of measurement in x, y, z and t are 2.5%, 2%, 0.5% and 1% respectively. The percentage error in Q will be
Options:
A) 5%
B) 4.5%
C) 8%
D) 7.75%
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Given: $ Q={{x}^{2/5}}{{y}^{-1}}{{t}^{-1/2}}z^{3} $
$ \therefore \frac{\Delta Q}{Q}\times 100 $
$ =\frac{2}{5}\frac{\Delta x}{x}\times 100+\frac{\Delta y}{y}\times 100 $
$ +\frac{1}{2}\frac{\Delta t}{t}\times 100+3\frac{\Delta z}{z}\times 100 $
$ =\frac{2}{5}\times 2.5+2+\frac{1}{2}\times 1+3\times 0.5=5% $
