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

Hint: 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.