Q122 / 160 · TS EAMCET 2023 (14 May Shift 2) · Physics

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

  • A
    $8 \%$
  • B
    $10 \%$
  • Correct answer
    C
    $12 \%$
  • D
    $14 \%$

Solution

Given quantity $X=\frac{2 k^3 1^2}{m \sqrt{n}}$ and percentage error in the measurement of $\mathrm{k}=1 \%, \mathrm{l}=2 \%, \mathrm{~m}=3 \%$ and $\mathrm{n}=$ $4 \%$ therefore value of $\mathrm{X}$ is uncertain by $3 \times 1+2 \times 2+1$ $\times 3+\frac{1}{2} \times 4=12 \%$

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

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