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A physical quantity is given by X=[M^(a)...

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, beta, gamma` respectively. Then the maximum % error in the quantity `X` is

A

aalpha+b"beta+cgamma`

B

aalpha+b"beta-cgamma`

C

`(a)/(alpha)+(b)/(beta)+(c)/(gamma)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`X=M^(a)L^(b)T^(c)`
Percentage error in X
`(DeltaX)/(X)=a(DeltaM)/(M)+b(DeltaL)/(L)+c(DeltaT)/(T)`
`(DeltaX)/(X)xx100=a(DeltaM)/(M)xx100+b(DeltaL)/(L)xx100+c(DeltaT)/(T)xx100`
As given, `(DeltaM)/(M)xx100=alpha,(DeltaL)/(L)xx100=beta,(DeltaT)/(T)xx100=gamma`
`:.` Percentage error in `X=alpha+b""beta+cgamma`
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