A cylindrical container of length `L` is full to the brim with a liquid which has mass density `rho`.it is placed on a weight -scale, the scale reading is `W`. A light ball of volume `V` and mass `m` which wold float on the liquid, if allowed to do so, is pushed gently downand held beneath the surface of the liquid with a rigid rod of negligible volume as shwon on the left.
What is the reading of the scale when the ball is fully immersed?
If instead of being pushed down by the rod, the ball is held in place by a thin string attached to the bottom of the containier as shown on the right.

Options

A. `W-rhoVg`
B. `W`
C. `W+mg-rhoVg`
D. none

Answer

B

Explanation

Let force `F` is to be applied on the rod to hold it.
`F+mg=B`
`impliesF=B-mg`
`impliesF=Vrhog-mg`
Now reading of the scale:

`W'=F+`weight of ball `+` weight of the remaining liquid
`=(Vrhog-mg)+mg+(W-Mg)`
`=Vrhog+W-Vrhog=W`
Alternatively: Reading of the scale will be net fore applied by liquid on the container, which will be the same in both cases.