You have given the answer but neither in the question nor in the answer you have mentioned what is K? If K is the mass per unit length then only the answer given by you will match with velocity units. If you say that it is so then your answer is lacking the relation between velocity and hanging length ( x) of the chain.

 

And if you say that k is length of the hanging portion of the chain then the units will not match with that of the velocity!

 

Now it is your turn to verify what is correct!

 

A heap of chain is lying on a horizontal table.A small section of the chain is released through a hole in the table. calculate the velocity as a function of the length of the chain hanging vertically.

 

 

sorry!!this is not the given answer.The correct answer is (2mg/k)^1/2