Question

When two quantities are divided, the relative error in the
result is given by
(a) the product of the relative error in the individual
quantities
(b) the quotient of the relative error in the individual
quantities
(c) the difference of the relative error in the individual
quantities
(d) the sum of the relative error in the individual
quantities​

Answer 1

Answer:

a)the product of the relative error in the inindividual quantities

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Answer 2

Answer is The sum of relative error in the individual

Explanation:

Combination of errors: When physical quantities involving a mathematical operation have errors associated with them, there will be an error in the result arising from its combination.

This is identified based on the following rules:

• The error of a sum or a difference: If ​two physical quantities A and B have measured values A ± ΔA, B ± ΔB respectively where ΔA and ΔB are their absolute errors, the possible error ΔZ in the operation Z = A ± B is given by:

                                     ± ΔZ = ± ΔA ± ΔB

• The error of a product or a quotient: If ​two physical quantities A and B have measured values A ± ΔA, B ± ΔB respectively where ΔA and ΔB are their absolute errors, the possible error ΔZ in the operation Z = AB or Z = A ÷ B is given by:

                    Δ Z Z = Δ A A + Δ B B ΔZZ=∆AA+∆BB

• The error in case of a measured quantity raised to a power: ​If Z = Ax then  Δ Z Z = x Δ A A ΔZZ=xΔAA EXPLANATION: When two quantities A and B are multiplied or divided, the error in their result Z is given by:

                       Δ Z Z = Δ A A + Δ B B ΔZZ=∆AA+∆BB.

So, the relative error in their result is the sum of the relative errors in the two quantities.

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