Q: A spherical steel ball released at the top of a long column of glycerin of length l falls through a distance 1/2 with accelerated motion and the remaining distance 1/2 with uniform velocity. Let t_{1} and t_{2} denote the times taken to cover the first and second half and W_{1} and W_{2} are the work done against gravity in the two halves, then compare times and work done.

Sol: Average velocity in first half of the distance < v, while in the second half the average velocity is v. Therefore, t_{1} > t_{2}. The work done against gravity in both halves is mg l/2

∴t_{1} > t_{2} ∴ W_{1} = W_{2}