Certainly! Let's walk through the problem step by step to find how much the solid will weigh in a liquid with a specific gravity of 0.9.
1. Weight in Air and Water:
- The weight of the solid in air is given as [tex]\(32 \, \text{gf}\)[/tex].
- The weight of the solid when immersed in water is [tex]\(28.8 \, \text{gf}\)[/tex].
2. Loss of Weight in Water:
- The loss of weight when the solid is immersed in water is equal to the weight of the water displaced by the solid.
- The loss of weight can be calculated by subtracting the weight in water from the weight in air:
[tex]\[
\text{Weight Displaced by Water} = 32 \, \text{gf} - 28.8 \, \text{gf} = 3.2 \, \text{gf}
\][/tex]
3. Specific Gravity of the Liquid:
- The specific gravity of the liquid is given as [tex]\(0.9\)[/tex].
- Specific gravity is the ratio of the density of the liquid to the density of water.
4. Weight Displaced by the Liquid:
- To find the weight of the liquid displaced by the solid, we multiply the weight of the water displaced by the specific gravity of the liquid:
[tex]\[
\text{Weight Displaced by Liquid} = 3.2 \, \text{gf} \times 0.9 = 2.88 \, \text{gf}
\][/tex]
5. Weight of the Solid in the Liquid:
- The weight of the solid when it is immersed in the liquid will be its weight in air minus the weight of the liquid displaced:
[tex]\[
\text{Weight in Liquid} = 32 \, \text{gf} - 2.88 \, \text{gf} = 29.12 \, \text{gf}
\][/tex]
So, the weight of the solid in a liquid with a specific gravity of 0.9 is [tex]\(29.12 \, \text{gf}\)[/tex].
