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While I was thinking about how tidal forces can make objects float at the surface of a planet orbiting a massive object like a black hole, the fact that any material on the Earth isn't held together by gravity only, but also by chemical bonds which give it its tensile strength came into my mind.

The scenario I thought of is as following:

Here is a simple picture to summarize:

Now, if we move the Earth to orbit the black hole even closer until the tidal forces on Earth due to the black hole become Δa = 10.8 m/s

In other words, if

The scenario I thought of is as following:

**1-**A**10 kg**metal sphere is tied to a 1 meter long thin rope and this rope is nailed into the surface of the Earth.**2-**The tensile strength of the rope is**10 N**. (So the metal sphere has to accelerate at 1 m/s^{2 }to break the rope)**3-**The Earth is orbiting a black hole at its Roche radius, and so our metal sphere on the surface of the Earth is effectively weightless and floating, but it is still held by the rope.Here is a simple picture to summarize:

Now, if we move the Earth to orbit the black hole even closer until the tidal forces on Earth due to the black hole become Δa = 10.8 m/s

^{2}and so the metal sphere is pulled by the difference between Δa and the Earth's gravitational acceleration (9.8 m/s^{2}) which is 1 m/s^{2}*towards the BH*, will the rope break or not ?In other words, if

**a**is the gravitational acceleration towards the BH, in order to break the rope, which one do we need ? :**1-**a (Point A) - a (Point B) = 1 m/s^{2}**OR****2-**a (Point A) - a (Point C) = 1 m/s^{2}[/SUP]
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