A cylindrical container of lenghtL is full to the brim with a liquid which has mass densityp. It is placed on a weigh-scale; the scale reading isW. A light ball which would float on the liquid if allowedto do so, of volume V and mass m is pushed gentlydown and held beneath the surface of the liquid with a rigid rod ofnegligible volume.
(a) What is the mass ofthe liquid which overflowed whilethe ball was being pused into the liquid?
(b) What is the reading of the scale when the ball isfully immersed after the water that overflowed has been removedfrom the scale?
(c) If instead of being pushed down by rod, theball is held in place by a thin tring attached to the bottom of thecontainer. What is the tension T in the string, and whatis the reading on the scale after the water that overflowed hasbeen removed from the scale?
I think that for part a the answer would be m=pV because
V=volume of ball = volume of water displaced
and p=m/v
I'm stuck on parts b and c. For part b I started solving it andit seems that the ball wouldn't exert any force on the scale.
Another solution that I came up with is that the force boyancywoud need an equal and opposite reaction force- from newtons laws.Then the scale would read: W-pV+force boyancy?
For part c I'm really stuck. It's in an equilibrium so: forceboyancy= tension+ weight?
