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

The statistical uncertainty of this measurement is 0.3 s.

(A) is correct option.

Step-by-step 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{((\mu)/(t_(1)))^2+((\mu)/(t_(2)))^2+((\mu)/(t_(2)))^2}`

Put the value into the formula

`uncertainty=\sqrt{((0.4)/(4.8))^2+((0.4)/(8.2))^2+((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.