Question

In making an alloy a substance of specific gravity ${s_1}$ and mass ${m_1}$ is mixed with another substance of specific gravity ${s_2}$ and mass ${m_2}$ ; then the specific gravity of the alloy is:
A. $\left( {\dfrac{{{m_1} + {m_2}}}{{{s_1} + {s_2}}}} \right)$
B. $\left( {\dfrac{{{s_1}{s_2}}}{{{m_1} + {m_2}}}} \right)$
C. $\dfrac{{{m_1} + {m_2}}}{{\left( {\dfrac{{{m_1}}}{{{s_1}}} + \dfrac{{{m_2}}}{{{s_2}}}} \right)}}$
D. $\dfrac{{\left( {\dfrac{{{m_1}}}{{{s_1}}} + \dfrac{{{m_2}}}{{{s_2}}}} \right)}}{{{m_1} + {m_2}}}$

Answer 1

Before proceeding to the question, let us first have a basic idea of the term related to the query that is specific gravity. The specific gravity of an object is the ratio of its density to that of a reference substance. The specific gravity can inform us whether an object will sink or float in our reference substance depending on its value. Water is commonly used as a reference substance since it has a density of 1gram per millilitre or 1 gram per cubic centimetre.

Complete step by step answer:
Now, coming to the question;
Specific gravity of alloy is given by;
$= \dfrac{{Density\,of\,alloy}}{{Density\,of\,water}}$
$= \dfrac{{Mass\,of\,alloy}}{{Volume\,of\,alloy \times Density\,of\,water}}$
$= \dfrac{{{m_1} + {m_2}}}{{\left( {\dfrac{{{m_1}}}{{{\rho _1}}} + \dfrac{{{m_2}}}{{{\rho _2}}}} \right) \times {\rho _w}}}$
Proceeding further in the equation;
$= \dfrac{{{m_1} + {m_2}}}{{\dfrac{{{m_1}}}{{\dfrac{{{\rho _1}}}{{rh{o_w}}}}} + \dfrac{{{m_2}}}{{\dfrac{{{\rho _2}}}{{rh{o_w}}}}}}}$
$= \dfrac{{{m_1} + {m_2}}}{{\left( {\dfrac{{{m_1}}}{{{s_1}}} + \dfrac{{{m_2}}}{{{s_2}}}} \right)}}$
Therefore the specific gravity of the alloy is $\dfrac{{{m_1} + {m_2}}}{{\left( {\dfrac{{{m_1}}}{{{s_1}}} + \dfrac{{{m_2}}}{{{s_2}}}} \right)}}$
So, the correct option is: C. $\dfrac{{{m_1} + {m_2}}}{{\left( {\dfrac{{{m_1}}}{{{s_1}}} + \dfrac{{{m_2}}}{{{s_2}}}} \right)}}$ .

Note:
Specific gravity is widely used in chemical science and technology due to its ease of measurement; for example, determining the specific gravity is part of the standard characterisation of a new liquid compound. Most organic molecules having solely carbon, hydrogen, and oxygen have a specific gravity of less than one. The Westphal balance, pycnometer, and hydrometer are examples of equipment used to measure specific gravity.