Question

A plate has a length (5+-0.1)cm&breadth (2+-0.01)vm. Then the area of the plate is

Answer 1

Answer:

Area of plate = (10+-0.25)cm².

Explanation:

Area of plate = length×breadth= 5×2=10 cm²/ 0.05×0.02=0.001 m²

Above area value we calculated is by using true valu or mean value as given in question { i.e., 5 of 5+-0.1 and 2 of 2+-0.01 both are multiplied}.

Since this is a question of error as in question both length and breadth has mean absolute error as 0.1 and 0.01, our final answer of area will also have error.

So to calculate error in area we apply formula of fractional error i.e.,

∆A/A= ∆l/l + ∆b/b

• ∆A= mean absolute error in area.

• A= mean value of area (that we have calculated above that is 10cm²)

• ∆l = mean absolute error in length(given in question that is +-0.1cm).

• l = mean value of length (given in question that is 5cm).

• ∆b = mean absolute error in breadth ( given in question that is +-0.01cm).

• b = mean value of breadth ( given

in question that is 2cm).

Put all the values in above formula:-

∆A/10 = 0.1/5 + 0.01/2

or, ∆A = 0.25cm²

Note:- Mean absolute error always has dimension and unit so in final value don't forget to write unit.

So we got our error in our area that is 0.25cm²

So final representation will be:-

Area of plate= (10+-0.25)cm²

I hope it help... feel free to ask any doubt related to solution in comments..

Answer 2

Answer:

A plate has a length (5+0.1) cm and breadth

(2.0 +0.01) cm. Then the area of the plate is