Statement I: The bob of a simple pendulum is a ball full of water. If a fine hole is made at the bottom of the ball, then the time period will no more remain constant.
Statement II: The time period of simple pendulum does not depend upon mass.

In initial position the ball is completely filled with water, CG of the ball is at the centre. When water flows out of the ball the centre of gravity comes down the centre of the ball. 

So, the effective length of the ball increase, hence the time period of pendulum also increases. After\ the water is completely drained, centre of mass of ball is at its geometric centre. So, effective length of pendulum decreases and the time period of pendulum also decreases hence, time period does not remain constant. We also know that time period of a simple pendulum does not depend upon the mass of bob as obvious from relation $T = 2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\mathrm{g}}}$.