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 is the velocity of heavier dust particle as compared to lighter dust particle is

The question is asking for a comparison of the uncertainties in the velocities of two dust particles with different masses but the same uncertainty in position. This is a problem related to Heisenberg's Uncertainty Principle in quantum mechanics, which states that the more precisely the position of a particle is known, the less precisely its momentum (and therefore its velocity) can be known, and vice versa.

The formula for Heisenberg's Uncertainty Principle is:

Δx * Δp ≥ h/4π

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

We can express the uncertainty in momentum as the product of the mass of the particle and the uncertainty in velocity (Δv):

Δp = m * Δv

Substituting this into the formula for the Uncertainty Principle gives:

Δx * m * Δv ≥ h/4π

Solving for Δv gives:

Δv ≥ h/(4π * m * Δx)

Given that Δx is the same for both particles, the uncertainty in velocity is inversely proportional to the mass of the particle. Therefore, the heavier particle (0.5 mg) will have a smaller uncertainty in velocity compared to the lighter particle (0.1 mg).