A wire has a mass 0.3 ± 0.003g, radius 0.5 ± 0.005mm and length 6 ± 0.06cm. The maximum percentage error in the measurement of its density is

Correct answer: D. 4 Density ρ = m ^ 2 L ∴ (∆ ρ)/(ρ) × 100 = ((∆ m)/(m) + 2(∆ r)/(r) + (∆ L)/(L)) × 100 After substituting the values we get the maximum percentage error in density = 4%

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Units and Dimensions

NTA Abhyas 2020 · Physics · Units and Dimensions

A wire has a mass 0.3 ± 0.003g, radius 0.5 ± 0.005mm and length 6 ±...

A wire has a mass

0.3 \pm 0.003g,

radius

0.5 \pm 0.005mm

and length

6 \pm 0.06cm.

The maximum percentage error in the measurement of its density is

Options

A $1$
B $2$
C $3$
D $4$

Correct answer

D. $4$

Step-by-step solution

Density

ρ = \dfrac{m}{\pir^{2}L}

∴ \dfrac{∆ ρ}{ρ} \times 100 = \left(\dfrac{∆ m}{m} + 2\dfrac{∆ r}{r} + \dfrac{∆ L}{L}\right) \times 100

After substituting the values we get the maximum percentage error in density = 4%

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