Question

If kinetic energy of particle is decreased by 2%, the percentage change in momentum is

Answer 1

1/4 because 1/2^2=1l4

Answer 2

Given: kinetic energy of particle is decreased by 2%.

To find:  the percentage change in momentum.

Solution:  By convention, since not mentioned specifically, we assume the mass to be constant.

We know by the relationship between kinetic energy and momentum that:

                     p = √2m K.E.

                     p ∝ √K.E.

By applying the concept of error analysis, we have:

             Δp / p = 1/2 × ΔK.E. / K.E.

  100 × Δp / p = 1/2 ×  ΔK.E. / K.E. × 100

  100 × Δp / p = 1/2 × - 2%       [given]

  100 × Δp / p = - 1%

Hence, the percentage change in momentum is - 1%.