A body of density d floats half immersed in a liquid. Will a body of same dimension but density 2d float in it?

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Solution

Given, both bodies have same dimension, meaning, density is changed but volume is constant.

Let , before density is changed
old density = d
Old mass = m
Old force = f, due to weight of body.

This force is balanced by buoyancy when body is half submerged.

Density = mass / volume. Mass= density × volume

New density = 2 ×d
hence new mass,

M = 2d × V.
As V is unchanged,
New mass = M = 2 × old mass ,
as old mass, m = d × v.

Mass has doubled, when density doubled.
New Force acting downwards= mass g = 2mg = 2 old force = 2f.

Buoyant force = weight of watet displaced.
When density was d, downward force f = mg acted and was balanced when half solid was submerged. Now, new force is 2* f. So, body must submerge twice as before to balance the new double weight, by displacing double the amount of water.

Before density increase, body was submerged half. So when density doubles, body submerges fully.

The body will float, but under the water. The body will be submerged, but as downward 2f is balanced now, as body submerges twice the initial, the body, if undisturbed , will float under water.

Hope you understand. If not,please ask another question . Thanks.

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