The mass of a photon is said to be 0, But light (photons) get attracted due to gravity of a black hole, that means photons have a mass which is very very very small. And we know that any object with mass cannot reach speed of light. Then how does a photon which have a very little mass can travel with speed of light?
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1"that means photons have a mass" - Welcome New contributor Gyan Prakash! Are you thinking of Newtonian gravity here? It's known in GR that gravity is spacetime curvature, and photons simply follow light-like geodesics of the (curved) spacetime. – Alfred Centauri Aug 19 '19 at 14:17
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3Possible duplicate of How is light affected by gravity? – Azzinoth Aug 19 '19 at 14:44
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1Light has no mass. It has energy and momentum though and it is all you need to be attracted by gravity. – J. Manuel Aug 19 '19 at 15:31
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In Newtonian mechanics, Black holes simply don't exist. Light doesn't have very small mass, it has exactly zero mass.
And in 1916, Albert Einstein gave his General theory of relativity, which fundamentally changed our definition of gravity. Now we don't see it as a force, but an absence of force. This is a strange idea, so I recommend go through the web or read a book to understand it better.
And this explains any object, doesn't matter if it has mass or not, can be affected by gravity. It only needs to have energy, which light surely does. Thus, there exist some strange objects called black holes which have gravitational influence great enough that even light can't escape.
And light has no problem in reaching it's speed.
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@AlfredCentauri thank you for that link, really interesting information about Newtonian Black Holes :D – Nico Brenner Aug 19 '19 at 19:59