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

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

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

Text Solution

Verified by Experts

The correct Answer is:
A
`(Delta X)/(X) xx 100 = a (Delta M)/(M) % + b (Delta L )/(L) % + c (Delta T)/(T) %`
`" "=a alpha % + b beta %+ cgamma % `
`(Delta X)/(X) xx 100 = (a alpha + b beta + c gamma) %`
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Knowledge Check

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

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