A physical quantity ‘y’ is represented by the
Question:

A physical quantity ‘y’ is represented by the

formula $\mathrm{y}=\mathrm{m}^{2} \mathrm{r}^{-4} \mathrm{~g}^{\mathrm{x}} l^{-\frac{3}{2}}$

If the percentage errors found in y, m, r, l and g are 18, 1, 0.5, 4 and p respectively, then find the value of x and p.

  1.  5 and ± 2 

  2.  4 and ± 3

  3. $\frac{16}{3}$ and $\pm \frac{3}{2}$

  4. 8 and ± 2


Correct Option: , 3

Solution:

$\frac{\Delta \mathrm{y}}{\mathrm{y}}=\frac{2 \Delta \mathrm{m}}{\mathrm{m}}+\frac{4 \Delta \mathrm{r}}{\mathrm{r}}+\frac{\mathrm{x} \Delta \mathrm{g}}{\mathrm{g}}+\frac{3}{2} \frac{\Delta \ell}{\ell}$

$18=2(1)+4(0.5)+x p+\frac{3}{2}(4)$

$8=x p$

By checking from options.

$x=\frac{16}{3}, p=\pm \frac{3}{2}$ 

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