The uncertainty in the position of a flying dust particle of mass 0.1 mg is found to be 10–4 m. The uncertainty in the position of another flying dust particle of mass 0.5 mg is also found to be same.The uncertainty in the velocity of lighter dust particle is nearly

The question is asking for the uncertainty in the velocity of the lighter dust particle. This can be found using Heisenberg's Uncertainty Principle, which states that the product of the uncertainties in the position and momentum of a particle is greater than or equal to a small constant. The formula is:

Δx * Δp ≥ h/4π

where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is Planck's constant.

First, we need to find the uncertainty in momentum (Δp) for the lighter dust particle. We know that momentum (p) is mass (m) times velocity (v), so Δp = m * Δv, where Δv is the uncertainty in velocity.

Rearranging the Uncertainty Principle formula for Δv gives us:

Δv = h / (4π * m * Δx)

We know that h = 6.63 * 10^-34 Js, m = 0.1 * 10^-6 kg (converted from mg to kg), and Δx = 10^-4 m. Plugging these values in gives us:

Δv = 6.63 * 10^-34 Js / (4π * 0.1 * 10^-6 kg * 10^-4 m)

Solving this gives us Δv ≈ 5.28 * 10^-25 m/s. So the uncertainty in the velocity of the lighter dust particle is approximately 5.28 * 10^-25 m/s.