To calculate the minimum uncertainty in the momentum of the object, we need to use the uncertainty principle, which states that the product of the uncertainty in position and the uncertainty in momentum is greater than or equal to the reduced Planck's constant, denoted as ħ.
a) Uncertainty in momentum (Δp) can be found using the formula:
Δp * Δx ≥ ħ
Where Δx is the uncertainty in position.
In this case, since the position of the object is not known, we can assume the uncertainty in position (Δx) to be equal to the length of the line, which is 2.5 m.
Δp * 2.5 ≥ ħ
To find the minimum uncertainty, we can assume Δp = ħ / 2. This gives us:
(ħ / 2) * 2.5 ≥ ħ
ħ * 2.5 / 2 ≥ ħ
1.25 ħ ≥ ħ
Therefore, the minimum uncertainty in momentum is equal to ħ, which is a fundamental constant with a value of approximately 1.05 x 10^(-34) kg·m/s.
b) Without additional information, it is not possible to determine the uncertainty in position or the specific value of momentum for the object. The uncertainty principle only provides a lower bound for the product of uncertainties.