This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Let's denote the length as L and the width as W. Given: Length L = (250 ± 1) mm Width W = (200 ± 1) mm From these values: Nominal length L_0 = 250 mm Absolute uncertainty in length L = 1 mm Nominal width W_0 = 200 mm Absolute uncertainty in width W = 1 mm a) What is the fractional uncertainty in its length? Step 1: Calculate the fractional uncertainty in length. The fractional uncertainty is given by ( L)/(L_0). Fractional uncertainty in length = 1 mm250 mm Fractional uncertainty in length = 0.004 The fractional uncertainty in its length is 0.004. b) What is the fractional uncertainty in its width? Step 1: Calculate the fractional uncertainty in width. The fractional uncertainty is given by ( W)/(W_0). Fractional uncertainty in width = 1 mm200 mm Fractional uncertainty in width = 0.005 The fractional uncertainty in its width is 0.005. c) What is the percentage error on its length? Step 1: Calculate the percentage error in length. The percentage error is the fractional uncertainty multiplied by 100\%. Percentage error in length = ( L)/(L_0) × 100\% Percentage error in length = 0.004 × 100\% Percentage error in length = 0.4\% The percentage error on its length is 0.4\%. d) What is the percentage error on its width? Step 1: Calculate the percentage error in width. Percentage error in width = ( W)/(W_0) × 100\% Percentage error in width = 0.005 × 100\% Percentage error in width = 0.5\% The percentage error on its width is 0.5\%. e) What is the area of one side of the book? State your answer with its uncertainty. Step 1: Calculate the nominal area (A_0). The area of one side of the book is A = L × W. A_0 = L_0 × W_0 A_0 = 250 mm × 200 mm A_0 = 50000 mm^2 Step 2: Calculate the fractional uncertainty in the area (( A)/(A_0)). For multiplication, the fractional uncertainties add up: ( A)/(A_0) = ( L)/(L_0) + ( W)/(W_0) ( A)/(A_0) = 0.004 + 0.005 ( A)/(A_0) = 0.009 Step 3: Calculate the absolute uncertainty in the area ( A). A = A_0 × (( A)/(A_0)) A = 50000 mm^2 × 0.009 A = 450 mm^2 Step 4: State the area with its uncertainty. A = (A_0 ± A) A = (50000 ± 450) mm^2 The area of one side of the book is (50000 ± 450) mm^2.