a beaker contains a saturated solution of sugar what will happen the the mass of the beaker

nothing -- it's still just a beaker

if you added a gram of sugar to the water in the beaker the mass of the beaker/fluid system increases by one gram

When a beaker contains a saturated solution of sugar, the mass of the beaker will remain the same. This is because in a saturated solution, the maximum amount of sugar that can be dissolved has already been dissolved in the liquid. Any additional sugar added will not dissolve, but rather remain as solid particles at the bottom of the beaker.

To understand why the mass remains the same, it's important to know that mass is a measure of the amount of matter in an object. In this case, the beaker itself is not changing in terms of the amount of matter it contains. The weight of the dissolved sugar molecules in the solution is already accounted for in the mass of the liquid.

However, it's worth noting that when the beaker is lifted, it may feel heavier due to the added weight of the solution compared to when it was empty. This is because the beaker is now holding both the liquid and the undissolved sugar particles.