Block A hangs by a cord from a spring balance and is submerg

Block A hangs by a cord from a spring balance and is submerged in a liquid contained in beaker. The mass of the beaker is 1.30 kg and the mass of the liquid is 2.15 kg. Balance D (the one holding it up) reads 3.85g and balance (the one holding the container with the liquid) reads 7.5 kg. the density of the liquid is 1.17 g/cm^3. what is the volume of block A?

Solution

Mass of block A

M_A=M_D+M_E-M_B-M_C =3.85+7.5-1.3-2.15 =7.9 kg

Forces on A

B+F_D-W_A=0

pV_Ag  +F_D-m_Ag=0

pV_Ag  +m_Dg= m_Ag

=>V_A =(m_A-m_D)/p =(7.9-3.85)/(1.17*10³)

V_A=3.46*10^-3 m³