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A necklace weighing 50g in air, but it weighs 46g in water. Assume copper is mixed with gold to prepare the necklace. How much copper is present in it? (Specific gravity of gold is 20 and that of copper is 10)
A) m = 25g
B) m = 30g
C) m = 35g
D) m = 20g

Last updated date: 20th Jun 2024
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Hint: Mass is defined as the measure of the amount of the matter in a body. Weight is defined as the measure of the force of gravity acting on the object. Specific gravity is defined as the ratio of the density of a substance to the density of a given material.

Complete step by step solution:
Given data:
Weight of the necklace in air = 50 g
Weight of the necklace in water = 46 g
The specific gravity of gold = 20
The specific gravity of copper = 10
Let m be the mass of the copper in the necklace.
Then the mass of the gold in the necklace is (50-m).
Let $V_1$ be the volume of copper and $V_2$ be the volume of gold respectively.
Thus the volume of copper, \[{V_1} = \dfrac{m}{{10}}\]
The volume of gold, \[{V_2} = \dfrac{{50 - m}}{{20}}\]
When immersed in water, $\rho = 1g/c{m^3}$
We know that decrease in weight = upthrust
\[ \Rightarrow \left( {50 - 46} \right)g = \left( {{V_1} + {V_2}} \right)\rho g\]
\[ \Rightarrow 4 = \dfrac{m}{{10}} + \dfrac{{50 - m}}{{20}}\]
\[\Rightarrow 80 = 2m + 50 - m\]
\[ \Rightarrow m = 30kg\]
Thus the mass of the copper in the necklace \[ = 30kg\].

Hence the correct option is B.

Note: 1. Specific gravity is also called relative density. The specific gravity of liquids is usually measured by a hydrometer. Specific gravity is a dimensionless quantity as it is a ratio. Relative density is also used to quantify the buoyancy of a substance either in a fluid or in a gas.
2. In weight, changes occur only when mass and gravity changes. Whereas the density changes whenever the pressure and temperature of the object changes.
3. Volume is defined as the amount of space that is occupied by the object.