Question

A beaker of mass 1.2 kg containing 2.5 kgof water rests on a scale.A 3.8 kg block ofa metallic alloy of density 3300 kg/m3is SuS-pended from a spring scale and is submergedin the water of density 1000 kg/m' as shownin the figure. What does the hanging scale read?acceleration of gravity is 9.8 m/5?Answer in units of N.

Answer 1

Givne data:

• The mass of beaker is ,m,=1.2 kg.

,

• The mass of water is ,m,'=2.5 kg.

,

• The mass of block is ,M,=3.8 kg.

,

• The density of water is ρb=3300 kg/m³.

The buoyancy force experienced by the block is given by,

`\begin{gathered} F_B=\rho_wV_bg \\ F_B=\rho_w\frac{M_{}}{\rho_b}g \\ F_B=(1000)(\frac{3.8_{}}{3300})(9.8) \\ F_B=11.28\text{ N} \end{gathered}`

Here, Vb is the volume of block, and ρw is the density of water.

The wieght of block will be,

`\begin{gathered} W^(\prime)=Mg \\ W^(\prime)=(3.8)(9.8) \\ W^(\prime)=37.24\text{ N} \end{gathered}`

Since the buoyancy force acts in upward direction and wieght of block acts in downward direction, therefore the net force experienced by the upper scale will be,

`\begin{gathered} W=W^(\prime)-F_B \\ W=37.24-11.28 \\ W=25.96\text{ N} \end{gathered}`

Thus, the upper scale will read 25.96 N of reading.

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