A physical quantity P is related to four observables a, b, c and d as follows: P= (a^(3)b^(2))/(sqrt(c)d)The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P?

A physical quantity P is related to four observables a, b, c and d as

1.	A physical quantity P is related to four observables a, b, c and d as follows: P= (a^(3)b^(2))/(sqrt(c)d)The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P?
Answer» <html><body><p>`12%`<br/>`13%`<br/>`15%`<br/>`16%`</p>Solution :As `P= (a^(3)<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>))/(sqrt(c)d)` <br/> The percentage error in P is <br/> `(<a href="https://interviewquestions.tuteehub.com/tag/deltap-2053537" style="font-weight:bold;" target="_blank" title="Click to know more about DELTAP">DELTAP</a>)/(P)xx100= [3((Deltaa)/(a))+ 2((Deltab)/(b))+ (1)/(2)((Deltac)/(c))+ (<a href="https://interviewquestions.tuteehub.com/tag/deltad-2053513" style="font-weight:bold;" target="_blank" title="Click to know more about DELTAD">DELTAD</a>)/(d)] xx <a href="https://interviewquestions.tuteehub.com/tag/100-263808" style="font-weight:bold;" target="_blank" title="Click to know more about 100">100</a>` <br/> `[ 3 xx 1%+ 2 xx 3%+ (1)/(2) xx 4%+ 2%]= 13%`</body></html>