A value for the acceleration of free fall on Earth is given as (10 ± 2) m s-2. Which statement is correct?

Question 13

A value for the acceleration of free fall on Earth is given as (10 ± 2) m s^-2.

Which statement is correct?

A The value is accurate but not precise.

B The value is both precise and accurate.

C The value is neither precise nor accurate.

D The value is precise but not accurate.

Reference: Past Exam Paper – November 2016 Paper 12 Q5

Solution:

Answer: A.

The ‘true’ value of the acceleration of free fall is 9.81 m s^-2.

From the value given in the question, the acceleration of free fall can be from (10 – 2 =) 8 m s^-2 to (10 + 2 =) 12 m s^-2.

The true value (= 9.81 m s^-2) lies within the range given by the uncertainty, and therefore the stated value is accurate. [C and D are incorrect]

Precision deals with how small or large the uncertainty is. A precise set of measurements would have a small scatter of readings. 

Here, the value is NOT precise as the uncertainty is large (relative to the mean value of 10).

Percentage uncertainty = 2/10 × 100% = 20 % (this is rather large)