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If the density of cylindrical red was measured by formula p= 4m/πd2 - l the percentage in error m d l are 2% 4% and 6% CALCULATE ERROR IN CALCULATED VALUE OF density.

If the density of cylindrical red was measured by formula p= 4m/πd2 - l the percentage in error m d l are 2% 4% and  6% CALCULATE ERROR IN CALCULATED VALUE OF density.

Grade:11

2 Answers

Rituraj Tiwari
askIITians Faculty 1792 Points
11 months ago
similar question
The density of cylindrical rod was measured by the formula ρ = 4m/πD^2l . The percentage errors in m, d, and l are 1%, 1.5% and 0.5%. Calculate the % error in the calculated value of density.

We know that

Density ρ = 4m/πD^2l

Now we know that

Δρ/ρ max = Δm / m + 2ΔD/D + Δl/l

But given Δm/m = 1% ΔD/D = 1.5% and Δl / l = 0.5%

Therefore maximum percentage error in the calculated value of density will be

Δρ/ρ max = 1% + 2 x 1.5% + 0.5%

= 1 + 3 + 0.5

=4.5%
saransh jain
18 Points
4 months ago

4.2%

Explanation:

Given The density of cylindrical rod was measured by the formula ρ = 4m/πD^2l. The percentage errors in m, d, and l are 1%, 1.5%, and 0.5%. Calculate the % error in the calculated value of density.

We know that

    Density ρ = 4m/πD^2l

Now we know that

     Δρ/ρ max = Δm / m + 2ΔD/D + Δl/l

 But given  Δm/m = 1% ΔD/D = 1.5% and Δl / l = 0.5%

Therefore maximum percentage error in the calculated value of density will be

   Δρ/ρ max = 1% + 2 x 1.5% + 0.5%

                    = 1 + 3 + 0.5

                     = 4.5%

 

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