Question

Two quantities
x1 = (3.0+ 0.1) S.l. unit
x2 = (6.0 +0.2) S.I. unit
are given and they are combined so that we find value of combination by x" = (X1X2)/Xq + X2

10. The value of x'' is

(1) (2.0 + 0.3) S.I. unit
(2) (2.0 + 0.2) S.I. unit
(3) (2.0 + 0.1) S.I unit
(4) (2.0 + 0.15) S.I unit​

Answer 1

Answer:

Option (1) (2 ± 0.3)

Explanation:

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Answer 2

Answer:

The value of x" is (2.0 + 0.1 ) S.I unit

Explanation:

Given:

x1 = (3.0+ 0.1) S.l. unit

x2 = (6.0 +0.2) S.I. unit

To find: The value of x"

Solution:

• The relative error in the result of a multiplication is the sum of the relative errors of the two numbers being multiplied
• The relative error in the division is the relative error in the numerator plus the relative error in the denominator.

Therefore

x' = $x_{1}+ x_{2}$

$x_{1}$ = (3.0+ 0.1)

$x_{2}$ = (6.0 +0.2)

$x_{1}+ x_{2}$ =  (3.0+ 0.1)  +(6.0 +0.2)

      X'     =( 9.0  + 0.3)

Relative error in two numbers

Δ$x_{1}$ = $\frac{0.1}{3.0}$

     = 0.033

Δ$x_{2} = \frac{0.2}{6.0}$

      = 0.033

Total error in the two numbers = 0.033 + 0.033

                                                   = 0.066

We have to write the answer in the absolute error then we need to multiply 18 by the relative error.

Absolute  error = value × relative error

Absolute error = 18  ×  0.066

                         = 1.188

Now we have to find the value of combination of x"

$x" = \frac{x_{1} x_{2} }{x_{1} + x_{2} }$

   = $\frac{(3.8 + 0.1)(6.0+0.2}{(9.0+0.3)}$

   = $\frac{(18.0+1.188}{(9.0 + 0.3)}$

Relative error in the numerator

$\frac{1.188}{18} = 0.066$

$\frac{0.3}{9.0} = 0.033$

Total error = 0.066 + 0.033 = 0.099

To To write the answer with an absolute error, we need to multiply the 2 by the relative error:

absolute error = Value ×relative error

absolute error  = 2× 0.099

                        = 0.198

$x" = \frac{x_{1} x_{2} }{x_{1} +x_{2} }$

    = $\frac{18.0+1.188}{9.0+0.3}$

    = 2 + 0.1

X" = 2 + 0.1

Final answer:

The value of x" is (2.0 + 0.1 ) S.I unit

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