A physical quantity is given by `X=["M"^(a)"L"^(b)"T"^(c)]`. The percentage error in measurement of M, L and T are `alpha,betaandgamma`, respectively. Then, the maximum % error in the quantity `X` is

Options

A. `a alpha+ beta +c gamma`
B. `a alpha +b beta-c gamma`
C. `a/(alpha)+b /(beta)+c/(gamma)`
D. none of these

Answer

A

Explanation

`X=M^(a)L^(b)T^(c)`, Percentae error in `X" "(DeltaX)/(X.)=a(DeltaM)/M+b(DeltaL)/L+c(DeltaT)/T`
`(DeltaX)/X xx 100=a(DeltaM)/Mxx100+b(DeltaL)/Lxx100+c(DeltaT)/Txx100`
As given `(DeltaM)/Mxx100=alpha, (DeltaL)/Lxx100=beta, (DeltaT)/Txx100=gamma`
`:.` Percentage error in `X=a alpha+b beta+c gamma`