Pls identify this round black gemstone.Specific gravity is about 3.20.hardness around 9 to 10

Question

Answer 1

Sapphires, rubies and diamonds are the only things that are 9-10 on the Mohs scale. If you are accurate that means it must be one of those. Diamond spec grav is 3.5, sapphire and ruby are close to 4.0. Diamonds are closest to both parameters.

Answer 2

That most certainly looks like obsidian - in the form popularly known as "apache tears". The color, habit, and strong conchoidal fracture clearly indicate that. I can't think of any other minerals or substances with the hardness you describe forming in this habit, so it's most likely you did not correctly perform the hardness test.

Comments

If it is obsidian the specific gravity won't be 3.20 right?   In order to identify a mineral which test must satisfy i. E specific gravity or harness test or surface texture?

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Correct, its usually lower and closer to 2.5. In order to identify a mineral just knowing a property like specific gravity and hardness can't identify it, but can assist in ruling out or identifying if you have a background on this. From visual perspective, the almost constant conchoidal fracture would indeed indicate obsidian or some other form of glass. Few other materials have such a distinct conchoidal fracture as the material you are showing in the picture.

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Is it anyway black serendibite? or schorl even?

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Highly unlikely - both those minerals have distinctive mineral faces almost invariably, and don't have that type of intensive conchoidal fracturing.