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. `(alpha a + beta b + gamma c) %`
B. `(alpha a- beta b + gamma c)%`
C. `(alpha a - beta b- gamma c)%`
D. None of these

Answer

A

Explanation

`X=M^(a)L^(b)T^(c)`
`rArr(DeltaX)/(X)=a((DeltaM)/(M))+b((DeltaL)/(L))+c((DeltaT)/(T))=a alpha+b beta+c gamma`