Question

The area of a square plate is calculated by measuring the length to be 5.5 cm. If

the scale used has a least count of 0.1 cm then what is the maximum percentage error

in the area?

Answer 1

Area = length X length    (because of square)

A = L2  

∂A/A  = 2 (∂L/L)

% error of A = 2 (% error of A)

% error of A = 2 (0.1/5.5) X 100

% error of A = 200/55 %

% error of A = 40/11 % = 3.64 %

is your Answer

Answer 2

Given that the area of a square plate is calculated, so the area of the square plate is being calculated by the square of the length of one side of the plate. Given is the least count being 0.1cm.

                    $Area = a={ L }^{ 2 }$

Therefore by differentiating we get,

                    $\frac { dA }{ A }=2\times\frac { dL }{ L }$

Therefore the percentage of error in the area be calculated by

                     % error of A = 2 (% error of A).

Given the data is least count be 0.1 cm and length be 5.5 cm, so the percentage error in

Area calculation = $2\times\frac { 0.1 }{ 5.5 }\times100$

                     $=\frac { 200 }{ 55 }$

                     $=\frac { 40 }{ 11 } =3.64 %$