Question

The length of a rod is $\left( 11.05\pm 0.2 \right)\,cm$ . What is the length of the two rods?
A. $\left( 22.1\pm 0.05 \right)\,cm$
B. $\left( 22.1\pm 0.1 \right)\,cm$
C. $\left( 22.10\pm 0.05 \right)\,cm$
D. $\left( 22.10\pm 0.4 \right)\,cm$

Answer 1

Hint: Here we have been given the length of a rod such that an error is shown by the “Plus or Minus’ sign we have to find the value of two such rods. Firstly we will let the length equal to any variable then we will add the length twice so as to get the length of two rods. Finally we will add the length and the error separately and get our desired answer.

Complete step-by-step solution:
The length of the rod is given as follows:
$\left( 11.05\pm 0.2 \right)\,cm$
We have to find the length of two rods by using the above length.
So let the length given be denoted as follows:
$T=\left( 11.05\pm 0.2 \right)\,cm$
Now we will find the value of $T+T$ as follows:
$T+T=\left( 11.05\pm 0.2 \right)\,cm+\left( 11.05\pm 0.2 \right)\,cm$
The length will be added separately and the error will be added separately as follows:
$T+T=\left( \left( 11.05+11.05 \right)\pm \left( 0.2+0.2 \right) \right)\,cm$
$\Rightarrow T+T=\left( 22.10\pm 0.4 \right)\,cm$
So the length of two rods is $\left( 22.10\pm 0.4 \right)\,cm$
Hence the correct option is (D).

Note: Length is used to measure the distance of any object or thing whose endpoints are known. It is the measurement or extent of anything from one end to another. It is the greatest value of a two or three dimensional object. In the International System of Units the (SI) base unit of length is meter. Measuring instruments are not always accurate. There is always a chance of error so this error can be shown in the form of “Plus or Minus'' sign $\pm $ . There are many other types of error such as Absolute error, relative error and Percentage error all of them are calculated differently.