The density of a cube is measured by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are 4 % and 3 %, respectively, then the maximum error in the measurement of the density is

Question

The density of a cube is measured by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are 4 % and 3 %, respectively, then the maximum error in the measurement of the density is (A) 9 % (B) 13 % (C) 12 % (D) 7 %

Tardigrade Admin · Accepted Answer

Density (ρ)=(Mass/Volume)=(m/l3) (Δρ/ρ)×100=(Δ m/m)×100+3 (Δ l/l)×100 =4 %+3×3 %=13 %

Q. The density of a cube is measured by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are $4%$ and $3%$ , respectively, then the maximum error in the measurement of the density is

$9%$

$13%$

$12%$

$7%$

Density $(ρ) = \frac{M a ss}{V o l u m e} = \frac{m}{l ^{3}}$
$\frac{Δ ρ}{ρ} \times 100 = \frac{Δ m}{m} \times 100 + 3 \frac{Δ l}{l} \times 100$
$= 4% + 3 \times 3% = 13%$

Q. The density of a cube is measured by measuring its mass and the length of its side. If the maximum errors in the measurement of mass and length are 4% and 3%, respectively, then the maximum error in the measurement of the density is

9%

13%

12%

7%