Can anyone point me to a library for 2D game physics, etc for programming gravity, jumping actions, etc for a 2d platform/sidescrolling game ? Or could you suggest some algo
If all you need is gravity, you can program that yourself in 5 minutes. Free-falling objects accelerate down at 9.8 meters per second per second - that is, an object's downward velocity increases by 9.8 meters per second of free-fall. For a game, you'll want to divide that 9.8 by whatever your frame rate is. For jumping, just pick a significant negative vertical velocity, apply that to the character at the instant they jump, and decrement it by your per-frame gravity increment. That's really all you need for something like Mario, unless you're looking for a 3d background for your 2d side scroller.
If you want to get fancier, you can try to take an object's impact force into account, making falling objects hurt people or crack pavement or something. For this, use the formula for Kinetic Energy: KE = 1/2 * M * V^2, where M is mass and V is velocity.