Question

The length of one rod is $l_1 = 3.323\,cm$ and the other is $l_2 = 3.321\,cm$. Both rods were measured with one measuring instrument with a least count of 0.001 cm. Then $\left( {{l_1} - {l_2}} \right)$ is

Answer 1

Hint: The lengths of the rods with the least count is found and then subtracted.

 

Complete step-by-step answer:

Least count of an instrument is the minimum value that we can measure with that instrument.

Length of rod one = $l_1 = (3.323 \pm 0.001)\;cm$

Length of rod two = $l_1 = (3.321 \pm 0.001)\;cm$

Here $\pm 0.001$ is added because of the least count of the instrument.

We have to find the value of $l_1 - l_2$

We also know that the errors always add up, so we get,

$\Rightarrow l_1 - l_2 = (3.323 \pm 0.001) - (3.321 \pm 0.001) = (0.002 \pm 0.002)\;cm$

 

Note: In such problems, one must be careful while considering the least count and other types of errors. The basic concepts should be clear. Mistakes can be avoided while subtracting and one must consider that the errors will add up.