A physical quantity `X` is represented by `X = (M^(x) L^(-y) T^(-z)`. The maximum percantage errors in the measurement of `M , L , and T`, respectively , are `a% , b% and c%`. The maximum percentage error in the measurement of `X` will be

Options

A. `(ax+by-cz)%`
B. `(ax-by-cz)%`
C. `(ax+by+cz)%`
D. `(ax-by+cz)%`

Answer

C

Explanation

`X=M^(x)L^(-y)T^(-z)`
`therefore (DeltaX)/(Y)xx100=x((DeltaM)/(M)xx100)+ underset("(Error are always added)")(y((DeltaL))/(L)xx100)+z((DeltaT)/(T)xx100)`
`therefore" "(DeltaX)/(X)xx100=(ax+by+cz)" per cent"`