Question

A piece of wax weighs $18.03\,g$ in air. A piece of metal is found to weigh $17.03\,g$ in water. It is tied to the wax and both together weigh $15.23\,g$ in water. Then, the specific gravity of wax is
A. $\dfrac{{18.03}}{{17.03}}$
B. $\dfrac{{17.03}}{{18.03}}$
C. $\dfrac{{18.03}}{{19.83}}$
D. $\dfrac{{15.03}}{{17.03}}$

Answer 1

We will first write the terms that are given in the question. After this, we will calculate the weight of wax in water by subtracting the weight of the metal from the weight of the combination. After that we will calculate the specific gravity of wax by using the relation given below.

Formula used:
The relation used for calculating the specific gravity of wax is given below
Specific gravity of wax $= \dfrac{{{w_{w1}}}}{{{w_{w1}} - {w_{w2}}}}$
Here, ${w_{w1}}$ is the weight of wax in air and ${w_{w2}}$ is the weight of wax in water.

Complete step by step answer:
The following are the terms that are given in the question,
Weight of wax in air, ${w_{w1}} = 18.03\,g$
Also, the weight of metal piece in water, ${w_m} = 17.03\,g$
Now, let both the wax and the metal are tied with each other, then
Weight of the combination is, ${w_{wm}} = 15.23\,g$
Now, we can calculate the weight of wax in water by subtracting the weight of the metal from the weight of the combination as shown below;
Weight of wax in water, ${w_{w2}} = 15.23 - 17.03$
${w_{w2}} = - 1.8\,g$
Now, the specific gravity of wax can be calculated as shown below;
Specific gravity of wax $= \dfrac{{{w_{w1}}}}{{{w_{w1}} - {w_{w2}}}}$
Here, ${w_{w1}}$ is the weight of wax in air and ${w_{w2}}$ is the weight of wax in water.
Now, substituting the values in the above equation we get,
$g = \dfrac{{18.03}}{{18.03 - \left( { - 1.8} \right)}}$
$\Rightarrow \,g = \dfrac{{18.03}}{{18.03 + 1.8}}$
$\therefore \,g = \dfrac{{18.03}}{{19.83}}$
Therefore, the specific gravity of wax is $\dfrac{{18.03}}{{19.83}}$.

Hence, option C is the correct option.

Note: To overcome the confusion between the weight of wax in water and weight of wax in air, we have denoted them as ${w_{w1}}$ and ${w_{w2}}$ respectively. Also, there is no need to convert the units, because the units in the denominator and the numerator are the same. Also, remember to mention all the terms given in the question.