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

Question

A wire has a mass (0.3 ± 0.003) g, radius (0.5 ± 0.005) cm and length (6 ± 0.06) cm. The maximum percentage error in the measurement of its density is (A) 1 % (B) 2 % (C) 3 % (D) 4 %

Tardigrade Admin · Accepted Answer

Density (ρ)=(m/π r2l) ∴ ((Δρ/ρ))×100=((Δ m/m)+2×(Δ r/r)+(Δ l/l))×100 =((0.003/0.3)+2×(0.005/0.5)+(0.06/6))×100 =(0.01+0.02+0.01)×100 =4 %

Q. A wire has a mass $(0.3 \pm 0.003) g$ , radius $(0.5 \pm 0.005) c m$ and length $(6 \pm 0.06) c m$ . The maximum percentage error in the measurement of its density is

$1%$

$2%$

$3%$

$4%$

Density $(ρ) = \frac{m}{π r ^{2} l}$
$∴ (\frac{Δ ρ}{ρ}) \times 100 = (\frac{Δ m}{m} + 2 \times \frac{Δ r}{r} + \frac{Δ l}{l}) \times 100$
$= (\frac{0.003}{0.3} + 2 \times \frac{0.005}{0.5} + \frac{0.06}{6}) \times 100$
$= (0.01 + 0.02 + 0.01) \times 100$
$= 4%$

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

1%

2%

3%

4%