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:

Question

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: (A) 0.31 (B) 0.10  (C) 0.07  (D) 0.01

Tardigrade Admin · Accepted Answer

Density (ρ )=(m a s s/v o l u m e) (Δ ρ /ρ )=(Δ m/m)+(Δ V/V) =(Δ m/m)+(3 Δ a/a) (∵ V = a3) =(0.1/10)+3((0.01/0.1)) =0.01+3(0.1) =0.31

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

$0.31$

$0.10$

$0.07$

$0.01$

Density $(ρ) = \frac{ma ss}{v o l u m e}$
$\frac{Δ ρ}{ρ} = \frac{Δ m}{m} + \frac{Δ V}{V}$
$= \frac{Δ m}{m} + \frac{3Δ a}{a}$ $(∵ V = a^{3})$
$= \frac{0.1}{10} + 3 (\frac{0.01}{0.1})$
$= 0.01 + 3 (0.1)$
$= 0.31$

Q. 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:

0.31

0.10

0.07

0.01