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

A spherical steel ball released at the top of a long column of glyceri

1.	A spherical steel ball released at the top of a long column of glycerine of length l falls through a distance l//2 with accelerated motion and the remaining distance l//2 with uniform velocity V. Let t_(1)andt_(2) denote the times taken to cover the first and second half and W_(1)andW_(2) the work done against gravity in the two halves, then compare times and work done.
Answer» Solution :The AVERAGE velocity in the first half of the distance `ltv`, while in the second half the average velocity is v. Therefore, `t_(1)gt t_(2)`. The work done against gravity in both HALVES is `mg l//2` `therefore t_(1)gtt_(2)w_(1)=w_(2)`