Question

A beaker of mass 1.1 kg containing 3.2 kg of
water rests on a scale. A 2.1 kg block of a
metallic alloy of density 5200 kg/m3
is suspended from a spring scale and is submerged
in the water of density 1000 kg/m3 as shown in the figure.
What does the hanging scale read? The
acceleration of gravity is 9.8 m/s2. Answer in units of N.

2.What does the lower scale read?
Answer in units of N.

Answer 1

Total mass on bottom scale

$$m=1.1+2.1=3.2\ kg$$

Volume of metal block

$$V=\frac{3.2}{5200}=6.15\cdot 10^{-4}\ m^3$$

Mass of water displaced

$$m_w=1000(6.15\cdot 10^{-4})=0.615\ kg$$

The hanging scale reading:

$$F_1=(3.2-0.615)(9.8)=25.33\ N$$

The lower scale reading

$$F_2=(3.2+0.615)(9.8)=37.39\ N$$