A neckless weighing 50 g in air, but it wheighs 46 g in water . Assume copper is mixed with gold to prepare the neckless. Find out how much of copper is present in it?(specific gravity of gold is 20 and that of copper is 10)
To find out how much copper is present in the necklace, we need to use the concept of specific gravity and the principle of buoyancy. Here's how you can calculate it step-by-step:
Step 1: Calculate the weight of the necklace in water.
The weight of the necklace in water is equal to the weight of the necklace in air minus the buoyant force acting on it. Since the buoyant force is equal to the weight of the water displaced by the necklace, we can use this formula:
Weight in water = Weight in air - Buoyant force
In this case, the weight in air is 50 g, and the weight in water is 46 g. Therefore, the buoyant force is:
Buoyant force = Weight in air - Weight in water
Buoyant force = 50 g - 46 g
Buoyant force = 4 g
So, the weight of the necklace in water is 46 g.
Step 2: Use specific gravity to determine the volume and weight of gold in the necklace.
The specific gravity of gold is 20, which means it is 20 times denser than water. Since the weight of the necklace in water is equal to the weight of the gold present in it, we can use this formula:
Weight of gold = Weight of necklace in water
Therefore, Weight of gold = 46 g.
Now, to find out the volume of gold, we can use the formula:
Volume of gold = Weight of gold / Density of gold
Since the density of gold is 20 times that of water, it is 20 g/cm3.
Using the formula:
Volume of gold = 46 g / 20 g/cm3 = 2.3 cm3
Step 3: Use the principle of conservation of mass to find the weight of copper in the necklace.
Since the necklace is a mixture of copper and gold, the weight of copper and gold combined should be equal to the weight of the necklace in air.
Weight of copper + Weight of gold = Weight of necklace in air
Weight of copper + 50 g = 50 g
Rearranging the equation:
Weight of copper = 50 g - Weight of gold
Weight of copper = 50 g - 46 g
Weight of copper = 4 g
Therefore, the weight of copper in the necklace is 4 g.
In conclusion, the necklace contains 4 g of copper.