Question

In an experiment, the percentage of error occurred In the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the
measurement X, where X = (A² B½) /(C¹/₃ D³) will be :
(1) (3/13)%
(2) 16%
(3) –10%
(4) 10%

Answer 1

The maximum percentage of error in the  measurement X is 16%

Step by step explanation:

From the given,

    $X=\frac{A^{2}B^{\frac{1}{2}}}{C^{\frac{1}{3}}D^{3}}$

The percentages of  error occurred in the physical quantities are as follows.

A = 1%

B = 2%

C = 3%

D = 4%

$\bold{Percentage\,of\,error,\frac{\Delta x}{x}\times 100=2\frac{\Delta A}{A}\times 100+\frac{1}{2}\frac{\Delta B}{B}\times 100+\frac{1}{3}\frac{\Delta C}{C}\times 100+3\frac{\Delta D}{D}\times 100}$Substitute the given values.

                                                  $\Rightarrow 2 \times 1 + \frac{1}{2}\times 2+\frac{1}{3}\times 3+3\times 4$

                                                  $\Rightarrow 16$

Hence, correct option is 2.