Question 138: Units , Dimensions and Error Analysis

Question

A physical quantity 'y' is represented by the formula $$y = {m^2}{r^{ - 4}}{g^x}{l^{ - {3 \over 2}}}$$
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.

Accepted Answer

$${{\Delta y} \over y} = {{2\Delta m} \over m} + {{4\Delta r} \over r} + {{x\Delta g} \over g} + {3 \over 2}{{\Delta l} \over l}$$
$$18 = 2(1) + 4(0.5) + xp + {3 \over 2}(4)$$
$$ \Rightarrow $$ 8 = xp
By checking from options.
$$x = {{16} \over 3},p =  \pm {3 \over 2}$$

Answer

5 and $$\pm$$2

Answer

4 and $$\pm$$3

Answer

$${{16} \over 3}$$ and $$ \pm {3 \over 2}$$

Answer

8 and $$\pm$$ 2

Units , Dimensions and Error Analysis

A physical quantity 'y' is represented by the formula $y = {m^2}{r^{ - 4}}{g^x}{l^{ - {3 \over 2}}}$ 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.

Choose the correct answer: