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If in a container full of water we place a ball of mass M and mass of water + container is m then what will be the weight measured by weighing machine if

A) the ball is completely immersed in water

B) ball is sinking but is held by a string from touching bottom

C) ball is half immersed

It might sound like a homework question but these questions popped in my head genuinely during a discussion and now my mind is highly confused whether when we should we consider buoyancy and so on..

Help appreciated

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The key point to note is that the weighing machine measures the total force exerted on it, which is equal to normal reaction exerted by the weighing machine on the container [along with the the mass inside].

If the mass is immersed partially or completely in the container with water, then the fluid (water) exerts an upthrust on the mass which is equal to the weight of the fluid displaced by the mass [Archimedes' principle]. Now the mass exerts a force equal and opposite to the upthrust on it [by Newton's third law]. This force adds to the normal reaction.

A) The total normal reaction in this case is the weight of the (container + fluid) + the upthrust on the mass (equal to the weight of the mass in this case since it is completely immersed. I have assumed that the mass does not touch the bottom of the container).

B) In this case the mass is balanced by both the upthrust and the tension in the string.

You can work out the remaining case similarly.

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  • $\begingroup$ So in case B) Normal would be lesser than first case? $\endgroup$ – Utkarsh futous May 20 '17 at 15:32
  • $\begingroup$ Yes, partly due to tension, the weight is balanced. $\endgroup$ – Tejas P May 20 '17 at 15:34

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