- #1

CaptCoonoor

- 19

- 0

## Homework Statement

So there is some water inside a container; the height of water inside the container is l. I placed a wooden block on the water and it's floating to some height x, on top of the block is a metallic coin (see the diagram below).

What will happen if I throw that coin inside the water? Will the Height x and l change? Can we derive an expression for this change? I tried doing it, but failed.

## Homework Equations

Fb=gρhA

## The Attempt at a Solution

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Here is what I've tried Let's assume that our wooden block has mass m1 Volume v1height h1, height underneath the water as y and let's assume mass of Metallic coin as m2 Now total mass on block will be equal to (in which buoyant force is actin upon) : m = m2 + m1 and let's also say that total height h1 = x + y

Principle of buoyancy of a liquid is Give as : Fb=gρhA

Simplifying :

Fb=g(m/v1)(x+y)A ... {1}

Now, archimedes principle is given as F=gρhA

F=g(ρf - ρb)hA // ρb is Density of the Body

And then I am not sure what to do next .. Can anyone help me out?