Due to more electrons in the same number of shells, the force of attraction from the nucleus will __ and the atom shrinks in size.

Due to more electrons in the same number of shells, the force of attraction from the nucleus will increase and the atom shrinks in size. 

In a period all elements have same number of shells. As we move from left to right in a period, the number of electrons goes on increasing. At the same time, the number of protons also goes on increasing, therefore attraction force of nucleus increases and pulls the valence electrons i.e. the outermost shell towards the nucleus and hence the size of atom goes on decreasing.