Question

If you were to measure the width of your lab manual with a meter stick, and then the length (roughly 50% longer), by what fraction would the absolute uncertainty differ in the two cases?
b) If you were to measure the width of your lab manual with a meterstick, and then the length (roughly 50% longer), by what fraction would the percent uncertainty differ in the two cases?

c) If you knew the radius of a circle with 1% accuracy, how accurate would your calculation of the area be?

Answer 1

Answer:

Explanation:

a )  Let breadth be L , then length will be 1.5 L

Since it is a meter scale , the least count is 1 m.m. So

maximum possible error in a measurement is 1 mm.

In both the measurement of length and breadth , absolute

uncertainty will be 1mm.

Hence there is no difference in  absolute uncertainty of their measurement.

b ) percent uncertainty in the measurement of length

$\frac{1 mm}{1.5L\times1000} \times100$

= 1 / 15L%

percent uncertainty in the measurement of breadth

$\frac{1 mm}{L\times1000} \times100$

1 / 10L%

In breadth it will be higher by

( 1/10L - 1/15L)/ 1/10L

= 1/3

c ) Uncertainty  in the measurement of R= 1 %

Area A = π R²

ΔA/A X100 = 2 X ΔR/R X 100

Percentage uncertainty in A = 2 X percentage uncertainty in R

= 2 X 1

=2 %

Therefore percentage  accuracy in the calculation of area

= 2 %.