A physical quantity Q is found to depend on quantities a, b, c by the relation Q=a^4b^3c^2. The percentage error in a, b and c are 3%, 4% and 5% respectively. Then, the percentage error in Q is:

Correct answer: (C) 34%. Given quantity is Q=(a^4b^3c^2.The relative error in measuring Q is given byΔQ)/Q=4(Δa)/a+3(Δb)/b+2(Δc)/c ...1 Hence, the required percentage error is given by (ΔQ)/Q×100 = 4(Δa)/a×100+3(Δb)/b×100+2(Δc)/c×100 = 4×3%+3×4%+2×5% = 12%+12%+10% = 34%

Q61 / 90 · JEE Main 2024 (29 Jan Shift 2) · Physics

A physical quantity $Q$ is found to depend on quantities $a, b, c$ by the relation $Q = \frac{a^{4} b^{3}}{c^{2}}$ . The percentage error in $a, b$ and $c$ are $3 %, 4 %$ and $5 %$ respectively. Then, the percentage error in $Q$ is:

A
$66 %$
B
$43 %$
Correct answer
C
$34 %$
D
$14 %$

Solution

Given quantity is $Q = \frac{a^{4} b^{3}}{c^{2}}$ .

The relative error in measuring $Q$ is given by

$\frac{Δ Q}{Q} = 4 \frac{Δ a}{a} + 3 \frac{Δ b}{b} + 2 \frac{Δ c}{c} . . . (1)$

Hence, the required percentage error is given by

$\begin{array}{rcl} \frac{Δ Q}{Q} \times 100 & = & 4 (\frac{Δ a}{a} \times 100) + 3 (\frac{Δ b}{b} \times 100) + 2 (\frac{Δ c}{c} \times 100) \\ = & 4 \times 3 % + 3 \times 4 % + 2 \times 5 % \\ = & 12 % + 12 % + 10 % \\ = & 34 % \end{array}$

Hence, the correct answer is option: 'C'.

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A physical quantity Q is found to depend on quantities a, b, c by the relation Q=a4b3c2. The percentage error in a, b and c are 3%, 4% and 5% respectively. Then, the percentage error in Q is:

Solution

Relevant Questions

A physical quantity $Q$ is found to depend on quantities $a, b, c$ by the relation $Q = \frac{a^{4} b^{3}}{c^{2}}$ . The percentage error in $a, b$ and $c$ are $3 %, 4 %$ and $5 %$ respectively. Then, the percentage error in $Q$ is: