The density of the material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 3.5 % and 1 %, then the maximum error in determining the density is %.

Question

The density of the material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 3.5 % and 1 %, then the maximum error in determining the density is %. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Density (ρ)=( text Mass / text Volume )=( m /l3) ....(. for cube .V =l3) Percentage relative error in density will be, (Δ ρ/ρ) × 100 =[(Δ m / m )+3 (Δ l/l)] % =[3.5+(3 × 1)] % =(3.5+3) %=6.5 %

Q. The density of the material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $3.5%$ and $1%$ , then the maximum error in determining the density is___________ $%$ .

Density $(ρ) = \frac{Mass}{Volume} = \frac{m}{l ^{3}} .... ($ for cube $V = l^{3})$
Percentage relative error in density will be,
$\frac{Δ ρ}{ρ} \times 100 = [\frac{Δ m}{m} + 3 \frac{Δ l}{l}] %$
$= [3.5 + (3 \times 1)] %$
$= (3.5 + 3) % = 6.5%$

Q. The density of the material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 3.5% and 1%, then the maximum error in determining the density is___________%.

Density (ρ)= Volume Mass ​=l3m​....( for cube V=l3) Percentage relative error in density will be, ρΔρ​×100=[mΔm​+3lΔl​]% =[3.5+(3×1)]% =(3.5+3)%=6.5%

Q. The density of the material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $3.5%$ and $1%$ , then the maximum error in determining the density is___________ $%$ .

Density $(ρ) = \frac{Mass}{Volume} = \frac{m}{l ^{3}} .... ($ for cube $V = l^{3})$
Percentage relative error in density will be,
$\frac{Δ ρ}{ρ} \times 100 = [\frac{Δ m}{m} + 3 \frac{Δ l}{l}] %$
$= [3.5 + (3 \times 1)] %$
$= (3.5 + 3) % = 6.5%$