A piece of brass (alloy of copper and zinc) weighs 12.9 g in air. When...
Concept:
- The Specific gravity of a substance is the ratio of its density to the density of water.
- A substance with a specific gravity of less than 1 will float in water. For example, an ice cube, with a relative density of about 0.91, will float. A substance with a specific gravity greater than 1 will sink.
- Whereas the relative density of a substance is defined as the ratio of densities of any two-sample, it can be expressed as
- Archimedes' principle states that when a body immersed in a fluid, whether fully or partially submerged, the upward buoyant force that is exerted on it, is equal to the weight of the fluid that the body displaces.
- Buoyant force: When an object is submerged in fluid fully or partially, an upward force is exerted on the body. This force is known as the buoyant force.
Calculation:
Given:
Mass of water displaced = 12.9 - 11.3 = 1.6 g
⇒ Volume of water displaced = mass / density = 1.6/1 = 1.6 cm3
We know that,
Relative density = density of substance / density of water
Since density of water = 1 g/cm3
⇒ Density of copper = 8.9 g/cm3
Let the mass of copper in 12.9 gram of alloy is x
Volume of water displaced by the copper = x/8.9 cm3
Similarly,
⇒ Density of zinc = 7.1 g/cm3
Also, the mass of zinc in alloy = 12.9 - x
Volume of water displaced by zinc = (12.9- x)/7.1 cm3
Hence total water displaced by the alloy,
Solving we get,
x = 7.614 gm.
Hence the mass of copper in the alloy is 7.614 gm.