# If the length of a cylinder is l = (4.00 ± 0.001) cm, radius r = (0.0250 ± 0.001) cm and mass m = (6.25 ± 0.01) g. Calculate the percentage error in the determination of density. - Physics

Numerical

Solve the numerical example.

If the length of a cylinder is l = (4.00 ± 0.001) cm, radius r = (0.0250 ± 0.001) cm and mass m = (6.25 ± 0.01) g. Calculate the percentage error in the determination of density.

#### Solution

Given:

l = (4.00 ± 0.001) cm,
In order to have same precision, we use,
(4.000 ± 0.001), r = (0.0250 ± 0.001) cm,
In order to have same precision, we use, (0.025 ± 0.001) m = (6.25 ± 0.01) g

To find: percentage error in density

Formulae:

1. Relative error in volume, (Delta"V")/"V" = (2Delta"r")/"r" + (Deltal)/l   ....(∵ Volume of cylinder, V = πr2l)

2. Relative error (Deltarho)/rho = (Delta"m")/"m" + (Delta"V")/"V"    ....[∵ Density (ρ) = ("mass"("m"))/("volume"("v"))]

3. Percentage error = Relative error × 100 %

Calculation:

From formulae (i) and (ii),

∴ (Deltarho)/rho = (Delta"m")/"m" + (2Delta"r")/"r" + (Deltal)/l

= 0.01/6.25 + (2(0.001))/0.025 + 0.001/4.000

= 0.0016 + 0.08 + 0.00025

= 0.08185

From formula (iii),

% error in density = (Deltarho)/rho xx 100

= 0.08185 × 100

= 8.185%

Percentage error in density is 8.185%.

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#### APPEARS IN

Balbharati Physics 11th Standard Maharashtra State Board
Chapter 1 Units and Measurements
Exercises | Q 3. (xii) | Page 15