A physical quantity is found to depend on quantities by the relation The percentage error in and are 3%, 4% and 5% respectively. Then, the percentage error in is

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Solution

Q.
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 [2024]

1 66%

2 14%

3 34%

4 43%

Ans.
(3)

   $\frac{∆ Q}{Q} = 4 \frac{∆ a}{a} + 3 \frac{∆ b}{b} + 2 \frac{∆ c}{c}$

   $Q = 4 \times 3 % + 3 \times 4 % + 2 \times 5 %$

$= 12 % + 12 % + 10 % = 34 %$

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