explain why calcium metal after reactin with water starts floating on its surface. write the chemical reaction for its reaction

Yes what you have given is correct.

Calcium metal reacts with water to forn calcium hydroxide and hydrogen gas. The reaction of calcium with water is less violent (compared to Na and K). The heat evolved is not sufficient for the hydrogen to catch fire.

Ca(s) + 2H2O(l)  → Ca(OH)2(aq)  +   H2(g)   + small amount of heat energy

  does not catch fire

Calcium starts floating on water because it becomes lighter due to the bubbles of hydrogen gas formed stick to its surface.