In the density measurement of a cube- the mass and edge length are measured as 10-00- 0-10 kg and 0-10- 0-01 m- respectively- The error in the measurement of density is

Density of cube = Mass of cubeVolume of cube ⇒ d=MV=ML^3=ML^ 3 Now error in density measurement, Δ dd=Δ MM+3Δ LL=0.1010.00+3 ( 0.010.10 )=0.31 kgm^ 3 Hence opti ...

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Standard XII

Physics

Addition & Subtraction of Errors

In the densit...

Question

In the density measurement of a cube, the mass and edge length are measured as $10.00 \pm 0.10 kg and (0.10 \pm 0.01) m$ , respectively. The error in the measurement of density is

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Solution

Density of cube $=$ $\frac{Mass of cube}{Volume of cube}$
$\Rightarrow d = \frac{M}{V} = \frac{M}{L^{3}} = M L^{- 3}$
Now error in density measurement,
$\frac{Δ d}{d} = \frac{Δ M}{M} + 3 \frac{Δ L}{L} = \frac{0.10}{10.00} + 3 (\frac{0.01}{0.10}) = 0.31 {kgm}^{- 3}$
Hence option $(C)$ is correct.

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In the density measurement of a cube, the mass and edge length are measured as 10.00±0.10 kg and (0.10±0.01) m, respectively. The error in the measurement of density is

Density of cube = Mass of cubeVolume of cube ⇒d=MV=ML3=ML−3 Now error in density measurement, Δdd=ΔMM+3ΔLL=0.1010.00+3(0.010.10)=0.31 kgm−3 Hence option (C) is correct.

In the density measurement of a cube, the mass and edge length are measured as $10.00 \pm 0.10 kg and (0.10 \pm 0.01) m$ , respectively. The error in the measurement of density is

Density of cube $=$ $\frac{Mass of cube}{Volume of cube}$
$\Rightarrow d = \frac{M}{V} = \frac{M}{L^{3}} = M L^{- 3}$
Now error in density measurement,
$\frac{Δ d}{d} = \frac{Δ M}{M} + 3 \frac{Δ L}{L} = \frac{0.10}{10.00} + 3 (\frac{0.01}{0.10}) = 0.31 {kgm}^{- 3}$
Hence option $(C)$ is correct.