Question

5. The time for a ball to fall is measured three times as 4.8 s, 8.2 s, and 7.4s all with the same uncertainty of +
0.4 s resulting from the human reaction time to start and stop the timer. What is the statistical uncertainty of
this measurement?
A. 0.3 s
B. 0.4 s
C. 0.7 s
D. 1.7 s

Answer 1

Answer:

The statistical uncertainty of  this measurement is 0.3 s.

(A) is correct option.

Explanation:

Given that,

Time for a ball to fall is measured three time as,

$t_{1}=4.8\ s$

$t_{2}=8.2\ s$

$t_{3}=7.4\ s$

The same uncertainty of ± 0.4 s.

We need to calculate the statistical uncertainty of  this measurement

Using formula of statistical uncertainty

$uncertainty=\sqrt{(\dfrac{\mu}{t_{1}})^2+(\dfrac{\mu}{t_{2}})^2+(\dfrac{\mu}{t_{2}})^2}$

Put the value into the formula

$uncertainty=\sqrt{(\dfrac{0.4}{4.8})^2+(\dfrac{0.4}{8.2})^2+(\dfrac{0.4}{7.4})^2}$

$uncertainty=0.1\ s$

The nearest answer will be 0.3 s.

Hence, The statistical uncertainty of  this measurement is 0.3 s.

(A) is correct option.