Question

If 1/x = 1/x1 + 1/x2 , where x, x1 and x2 are physical quantities with x1 = (60 ± 0.36); x2 = (30 ± 0.36), then x will be​

Answer 1

Given:

We have been given $\frac{1}{x} = \frac{1}{x_1}+\frac{1}{x_2}$ where $x, x_1$ and $x_2$ are the physical quantities and their values are

$x_1 = (60\pm0.36)$ and $x_2= (30\pm0.36)$

To find:

We have to find the value of the $x$.

Solution:

First of all we will find the value of real part and then the error part.

Considering the real part,

Now,

$x_1 + x_2 = 60 + 30 = 90$

Now by using the formula,

$x=\frac{x_1 x_2}{ x_1 + x_2}$

Putting the values in the above formula,

$\Rightarrow \frac{60\times30}{ 90 }\\\Rightarrow 2$

Considering the error part,

Again,

$\triangle x_1+\triangle x_2=0.36+0.36=0.72$

Again using the formula, we get

$\triangle x=\frac{\triangle x_1 \triangle x_2}{\triangle x_1 + \triangle x_2}$

$\Rightarrow \frac{0.36\times0.36}{0.72 }\\\Rightarrow 0.18$

Now, the required value is,

$x= 2\pm 0.18$.

Therefore, the value of $x= 2\pm 0.18$.