Y= 2π √(A/9.8m/s^2)
A = 10.8 +/- 0.2
Calculate Y and its uncertainty
To calculate Y and its uncertainty, we can use the formula:
Y = 2π √(A/9.8m/s^2)
Given that A = 10.8 +/- 0.2, we have the value of A and its uncertainty.
First, let's calculate the value of Y using the given value of A.
Y = 2π √(10.8/9.8m/s^2)
≈ 6.313 meters
Now, let's calculate the uncertainty in Y.
To find the uncertainty in Y, we need to consider the more significant effect of the uncertainty in A, which is ±0.2.
We can use the formula for percentage uncertainty:
Percentage uncertainty = (uncertainty / value) * 100
So, the percentage uncertainty in A is:
(0.2 / 10.8) * 100 ≈ 1.85%
To find the uncertainty in Y, we multiply the percentage uncertainty in A by the value of Y:
Uncertainty in Y = (Percentage uncertainty in A / 100) * Y
Uncertainty in Y = (1.85 / 100) * 6.313
Uncertainty in Y ≈ 0.117 meters
Therefore, Y = 6.313 +/- 0.117 meters.