Fluids Archimedes principle apparent weight question

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Homework Help Overview

The problem involves a vessel containing water on a balance, with a solid of specific gravity 1 suspended in the water. The discussion centers on the weight reading of the balance in two scenarios: when the solid is suspended independently and when it is tied to the balance arm.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the effects of buoyant force on the weight reading of the balance. Questions arise regarding the difference in readings between the two scenarios presented, particularly focusing on the implications of the solid's specific gravity being equal to that of water.

Discussion Status

Some participants have provided insights into the reasoning behind the weight readings, noting that the first part of the problem involves the buoyant force and its effect on the balance. However, there remains a focus on clarifying the second part of the question, with ongoing exploration of how the force on the vessel changes depending on the attachment of the thread.

Contextual Notes

Participants are considering the implications of the solid's density being equal to that of water, as well as the mechanics of torque and balance in the second scenario. There is an emphasis on understanding the underlying principles rather than arriving at a definitive answer.

sachin123
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Homework Statement

Vessel contains water.It is placed on the pan of a physical balance.A solid(specific gravity=1) is suspended from an thread(from an independent support),such that it is immersed completely in the water.
What the weight it reads?

If the thread was tied to the arm of the balance,what would the weight have been?

The attempt at a solution
First Part:
Water exerts a buoyant force on the solid.This results in a reaction force (equal and opposite).
Thus the weight read is that of vessel with water+solid.

Correct?
Second Part:
My book says it is equal to the weight of the vessel with water only.How it is so?How is it different from the first case?
 
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Although the answer is correct you shouldn't say the weight on the balance would be the weight of water plus that of the solid. Rather it is better to say that the reading shows the weight of water plus the weight of water that would have been enclosed in the solid had it been made of water. Here the density of solid is equal to that of water (a coincidence).
 
Okay.But what about the 2nd part.That is more important.Please read that too.
 
The weight reading is actually the force needed to balance the torque of the other arm. Since distances are equal from both sides this aspect is not important. But how do you suppose the force on the vessel changes if the thread were tied to the other end?
 

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