The percentage errors in quantities P , Q , R and S are 0.5 % , 1 % , 3 % and 1.5 % respectively in the measurement of a physical quantity A=(P3 Q2/√R S) . The maximum percentage error in the value of A will be:

Question

The percentage errors in quantities P , Q , R and S are 0.5 % , 1 % , 3 % and 1.5 % respectively in the measurement of a physical quantity A=(P3 Q2/√R S) . The maximum percentage error in the value of A will be: (A) 6.5 % (B) 7.5 % (C) 6.0 % (D)  8.5 %

Tardigrade Admin · Accepted Answer

100× ((Δ A/A))=((3 Δ P/P) + (2 Δ Q/Q) + (1/2) (Δ R/R) + (Δ S/S) )× 100 max percentage error, A=3 × 0.5+2 × 1+(1/2) × 3+1.5 =1.5+2+1.5+1.5 =6.5 %

Q. The percentage errors in quantities $P$ , $Q$ , $R$ and $S$ are $0.5%$ , $1%$ , $3%$ and $1.5%$ respectively in the measurement of a physical quantity $A = \frac{P ^{3} Q ^{2}}{R S}$ . The maximum percentage error in the value of $A$ will be:

$6.5 %$

$7.5 %$

$6.0 %$

$8.5 %$

$100 \times (\frac{Δ A}{A}) = (\frac{3Δ P}{P} + \frac{2Δ Q}{Q} + \frac{1}{2} \frac{Δ R}{R} + \frac{Δ S}{S}) \times 100$
max percentage error, $A = 3 \times 0.5 + 2 \times 1 + \frac{1}{2} \times 3 + 1.5$
$= 1.5 + 2 + 1.5 + 1.5$
$= 6.5 %$

Q. The percentage errors in quantities P , Q , R and S are 0.5% , 1% , 3% and 1.5% respectively in the measurement of a physical quantity A=R​SP3Q2​ . The maximum percentage error in the value of A will be:

6.5%

7.5%

6.0%

8.5%