A physical quantity X is given by X = $\frac{2 K^{3} l^{2}}{m \sqrt{n}}$ The percentage error in the measurement of k, l, m and n are 1 %, 2%, 3% and 4% respectively. The value of X is uncertain by

8%

10%

12%

None of these

Solution

12%

Given:-

X = $\frac{2 k^{3} l^{2}}{m \sqrt{n}}$

∴ $\frac{∆ X}{X} = 3 \frac{∆ k}{k} + 2 \frac{∆ l}{l} + \frac{∆ m}{m} + \frac{1}{2} \frac{∆ n}{n}$

Percentage error in X

$\frac{∆ X}{X} \times 100 = 3 \frac{∆ k}{k} + 2 \frac{∆ l}{l} + \frac{∆ m}{m} + \frac{1}{2} \frac{∆ n}{n}$

= 3 × 1% + 2 × 2% + 3% + $\frac{1}{2}$ × 4%

= 3% + 4% + 3% + 2%

⇒ $\frac{∆ X}{X} \times 100$ = 12%

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