Question

Upon completion of an experiment a student realizes that the technique used for measuring the length and width of a rectangle has a systematic error of 3.8 cm. (The measured length is always more than the actual length.) If the student found the most probable values of the width and length to be 85.7 cm and 123.5 cm, respectively; what is the systematic error of the area of the board

Answer 1

809.4cm²

Explanation:

Given the following :

Systematic error = 3.8cm (The measured length is always more than the actual length.)

Most probable dimension :

Width = 85.7 cm

Length = 123.5 cm

Hence most probable area of Rectangle :

Area = Length × Width

Area = 85.7cm × 123.5cm = 10583.95 cm²

Dimension due to Systematic error :

Length = (85.7cm + 3.8cm) = 89.5cm

Width = (123.5cm + 3.8cm) = 127.3cm

Area = Length × width

Area = ( 89.5cm × 127.3) = 11393.35cm²

Systematic error of the area :

value of area with Systematic error - Probable value of area :

11393.35cm² - 10583.95 cm² = 809.4cm²