Two solid pieces, one of steel and the other of aluminium when immersed completely in water have equal weights. When the solid pieces are weighed in air
(1) The weight of aluminium is half the weight of steel
(2) Steel piece will weigh more
(3) They have the same weight
(4) Aluminium piece will weigh more
please explain.  

Dear student

When an object is underwater, it has the force of gravity pulling it down and buoyant force pulling it up.  The force of gravity is determined by mass, and buoyant force is determined by volume.  
Since aluminium is less dense that steel, the aluminium piece has to be bigger than the steel block.  Since it's bigger, it has more buoyant force, so it needs to be even bigger to have the same  weight in water  as the steel. 
Once both are removed from the water, the buoyant force goes away.  The aluminium, having more volume, loses more buoyant force, and so becomes heavier in air.
So option (4) is correct.

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