A physical quantity X is related to four measurable quantities a,b,c and d as follows.
`X=a^2b^3c^(5//2)d^-2`
The percentage error in the measurement of a,b,c and d are `1%,2%,3%` and `4%` respectively. What is the percentage error in X?

Explanation

`X=a^(2)b^(3)c^(5//2)d^(-2)`
`(Deltaa)/a times 100=1%, (Deltab)/b times 100=2%, (Deltac)/c times 100=3%, (Deltad)/d times 100=4%`
Percentage error in X is
`((DeltaX)/X)100=2((Deltaa)/a times100)+3((Deltab)/b times 100)+5/2((Deltac)/c times 100)+2(Deltad)/d times 100`
`" "=2 times1+3 times 2+5/2 times 3+2 times 4=2+6+15/2+8 rArr ((DeltaX)/X)100=23.5%`