Physics, asked by samszy3321, 10 months ago

Percentage error in the measurment of height and radius of cylinder are x and y respectively. Find percentage error in the measurement of volume. Which of the two measurements height or radius needs more attention? Why?

Answers

Answered by Cosmique
18

Given :-

Percentage error in measurement of height ( h ) of cylinder is x

Percentage error in the measurement of radius ( r ) of cylinder is y

To find :-

percentage error in the measurement of volume of cylinder

Which of the two measurements height or radius needs more attention and why ?

Knowledge required :-

Volume of cylinder = π r² h

( where r is the radius and h is the height of cylinder )

↪ Error of a product or quotient

Let,   Z = AB

then,

Δ Z / Z = ( Δ A / A ) + ( Δ B / B )

↪ Error in case of a measured quantity raised to a power

Generally if

Z = Aᵃ Bᵇ

then,

Δ Z / Z = a ( Δ A / A ) + b ( Δ B / B )

Solution :-

According to the given information

(Δ h / h) × 100 % = x .... eqn(2)

(Δ r / r) × 100 % = y .... eqn(1)

we have to find

(Δ V / V) × 100 %

→  As we know,

Volume of cylinder ( V ) = π r² h

so,

(ΔV / V) = 2 ( Δ r / r ) + ( Δ h / h )

( multiplying by 100 % both sides )

(ΔV / V) ×100%= 2(Δr/r)×100%+(Δh/h)×100%

( using eqn (1) and (2)

(ΔV / V) × 100 % = 2 ( y ) + x

so,

(ΔV / V)×100% = 2 y + x   (Ans.)

●measurement of Radius needs more attention because its error will be doubled in this Case .

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