A physical quantity P depends on α ,β and γ as P=(α 2 β /γ 4). If the percentage error in the measurement of α ,β and γ are respectively 0.1 %,0.2 % and 0.4 %, then the maximum percentage error in the measurement of P is

Question

A physical quantity P depends on α ,β and &gamma; as P=(α 2 β /&gamma; 4). If the percentage error in the measurement of α ,β and &gamma; are respectively 0.1 %,0.2 % and 0.4 %, then the maximum percentage error in the measurement of P is (A) 1.2 % (B) 1.5 % (C) 2.0 % (D) 2.6 %

Tardigrade Admin · Accepted Answer

P=α 2(β /&gamma; 4) ⇒ (Δ P/P)× 100 =2((Δ α /α ) × 100)+((Δ β /β ) × 100)+4[(Δ &gamma; /&gamma; ) × 100] =2[.0.1].+0.2+4[.0.4]. =0.2+0.2+1.6=2.0 %

Q. A physical quantity $P$ depends on $α, β$ and $γ$ as $P = \frac{α ^{2} β}{γ ^{4}} .$ If the percentage error in the measurement of $α, β$ and $γ$ are respectively $0.1%, 0.2%$ and $0.4%,$ then the maximum percentage error in the measurement of $P$ is

$1.2%$

$1.5%$

$2.0%$

$2.6%$

$P = α^{2} \frac{β}{γ ^{4}}$
$\Rightarrow \frac{Δ P}{P} \times 100$
$= 2 (\frac{Δ α}{α} \times 100) + (\frac{Δ β}{β} \times 100) + 4 [\frac{Δ γ}{γ} \times 100]$
$= 2 [0.1] + 0.2 + 4 [0.4]$
$= 0.2 + 0.2 + 1.6 = 2.0%$

Q. A physical quantity P depends on α,β and γ as P=γ4α2β​. If the percentage error in the measurement of α,β and γ are respectively 0.1%,0.2% and 0.4%, then the maximum percentage error in the measurement of P is

1.2%

1.5%

2.0%

2.6%