Physics
An egg sinks in soft water but floats in a concentrated solution of salt because

The density of salt solution exceeds the density of eggs
Water has high surface tension
Albumin dissolves in salt solution and egg becomes lighter
Egg absorbs salt from the solution and expands

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Physics
On a clean glass plate a drop of water spreads to form a thin layer whereas a drop of mercury remains almost spherical because:

cohesion of water is greater than its adhesion with glass.
mercury is a metal.
density of mercury is greater than that of water.
cohesion of mercury is greater than its adhesion with glass.

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