A physical quantity Q is found to depend on quantities a, b, c by the relation Q= a4b3c2. The percentage error in a, b and c are 3\%, 4\% and 5\% respectively. Then, the percentage error in Q is :
- 43%
- 34%
- 66%
- 14%
Answer
(2) 34%
Solution
QQ 100=4 ( aa 100 )+3 ( bb 100 )+2 ( cc 100 )
=4(3\%)+3(4\%)+2(5\%)
=12\%+12\%+10\%=34\%
In a product or quotient, relative errors add, each multiplied by its power.
Answer: (2)