Answer

Verified

81.6k+ views

**Hint**Calculate the relative error by multiplying the powers of each of the variables with their percentage errors and adding their individual values.

**Complete step by step answer**

Percent error is calculated by dividing the difference between measured and known value with the known value, multiplied by $100\% $

Relative error is connected with the notion of correct significant digits or correct significant figures. The significant digits in a number are the first nonzero digit and all succeeding digits.

It gives us an idea about the size of the error in a particular physical quantity. The relative error does not have a unit because it is a ratio of the same physical quantity. Since it is a proportion, so we can express it as a percentage by multiplying the relative error by $100\% $

On the other hand absolute error is just the difference between the measured value and the true value unlike the relative error which is a ratio. So the absolute error has a unit.

The relative error in $P$ is given as

$

\dfrac{{\Delta P}}{P} = \dfrac{1}{2}\dfrac{{\Delta a}}{a} + 2\dfrac{{\Delta b}}{b} + 3\dfrac{{\Delta c}}{c} + 4\dfrac{{\Delta d}}{d} \\

\Rightarrow \dfrac{{\Delta P}}{P} = \left( {\dfrac{1}{2} \times 2} \right) + \left( {2 \times 1} \right) + \left( {3 \times 3} \right) + \left( {4 \times 5} \right) \\

\Rightarrow \dfrac{{\Delta P}}{P} = (1 + 2 + 9 + 20) \\

\Rightarrow \dfrac{{\Delta P}}{P} = 32\% \\

$

Therefore the relative error in $P$ is $32\% $

**So, the correct answer is D.**

**Note**Relative error has two features- Its value becomes undefined when the true value of the variable is zero.

-Relative error is only applicable when measured on a ratio scale.

Recently Updated Pages

Name the scale on which the destructive energy of an class 11 physics JEE_Main

Write an article on the need and importance of sports class 10 english JEE_Main

Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main

Choose the one which best expresses the meaning of class 9 english JEE_Main

What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main

A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main