Question

GIVE REASONS :1 Iron does not burn on heating but iron filings burnnvigorously when sprinkled in the flame of a burner

Answer 1

To burn  the surface of iron in contact with air must be heated to its ignition temperature. Iron has a strong molecular force of attraction. Hence when heated it doesn't reach to its ignition temperature and doesn't burn. But iron fillings  when sprinkled in flames attain the ignition temperature ( as iron fillings are comparatively smaller particles) and gain larger surface area for the reaction. Therefore they burn vigorously.

Answer 2

For burning to occur, the surface in contact with the air must be heated to its ignition temperature. ... An iron rod will not burn as it has relatively very less surface area per unit mass but ironfilings with more surface area per unit mass can burn in air and get converted to iron oxide.

There may be two possibilities for vigorous burning of iron fillings: 
The surface area of the fillings is much more than a block of iron. 
The heat supplied to the iron fillings does not have a way to distribute itself through conduction, like in iron block, as the entire filling is surrounded by the flame, and thus, the iron fillings reach their ignition temperature but iron block does not.