Hello Stephy,

Suppose the length of an element at distance x from the table is dx. Let us consider that the mass of the hanging part is at the center of the gravity. Work done(W) is,

W = (M/L)*dx*g(x), where g(x) is x. Total work done to pull 1/3 part on the table. 

W = integration of (M/L)*g(x)*dx with upper and lower limit as 1/3 and 0 respectively.  

After solving. Work done(W) = MgL/18.