Topic: Fluids
Concepts: Buoyant force, Newton’s laws, Scale reading

Solution:

Note that the scales determine mass by dividing their measured force by $g$. Thus, in the beginning, the first scale measures the normal force on itself as $F_1=M_1g$. The second scale measures its tension as $F_2=M_2g$.

Once the block is submerged in the water, the buoyant force $F_B$ acts upward on the block reducing the tension to $T=F_2-F_B$. By Newton’s 3rd law, the block also exerts a force $F_B$ down on the water so the normal force on the bottom increases to $N=F_1+F_B$.

By Archimedes’ principle, we have

where $V$ is the volume of the block. Since the block has mass $M_2$,

Substituting this back into $F_B$,

Then the mass measured by the first scale is

The mass measured by the second scale is

so the answer is E.