Grade 10Mechanics

A physical quantity is represented by X = M^a L^b T^c . If the percentage errors in measurements of M , L and T are alpha % , beta % and gamma % respectively , then what is the total percentage error on the measurement of physical quantity ?

Aiden Mathew Denny

8 Years agoGrade 10

2 Answers

Venkat

Approved Tutor Answer8 Years ago

Given X = M^aL^bT^c

Percentage error in X = (∆X/X)×100

= a(∆M/M)×100 + b(∆L/L)×100 + c(∆T/T)×100

But (∆M/M)×100 = α; (∆L/L)×100 = β; (∆T/T)×100 = γ

= ( aα + bβ + cγ )%

ankit singh

5 Years ago

Answer

Given, X=MηL−θT−ϕ

Differentiating, ΔX=(ηMη−1ΔM)L−θT−ϕ−(θL−θ−1ΔL)MηT−ϕ−(ϕT−ϕ−1ΔT)MηL−ϕ

So, XΔX=ηMΔM−θLΔL−ϕTΔT

As the error should be both positive and negative , so we can take mod

The % error in X =∣XΔX∣×100

=[ηMΔM+θLΔL+ϕTΔT]×100

=(ηα+θβ+ϕγ) %

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A physical quantity is represented by X = Ma Lb Tc . If the percentage errors in measurements of M , L and T are alpha % , beta % and gamma % respectively , then what is the total percentage error on the measurement of physical quantity ?

Aiden Mathew Denny

2 Answers

Venkat

ankit singh

Answer

Given, X=MηL−θT−ϕ

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