The composition of a liquid with suspended solid particles is generally characterized by the fraction of solid particles either by weight or mass, $C_{s,\text{m}\text{a}\text{s}\text{s}}=m_s+m_m,$ or by volume, $C_{s,\text{v}\text{o}\text{l}}=\frac{V_s}{V_m},$ where $m$ is the

mass and $V$ is the volume. The subscripts $s$ and $m$ indicate solid and mixture, respectively. Choose the right expression for the specific gravity of a water$-$based suspension in terms of $C_{s,\text{m}\text{a}\text{s}\text{s}}$ and $C_{s,\text{v}\text{o}\text{l}}.$

Multiple Choice

$S{G}_m=\frac{{}_m}{{}_f}=\frac{1+C_{s,\text{m}\text{a}\text{n}}}{1+C_{,\text{o}\text{u}\text{d}}}$

$S{G}_m=\frac{{}_m}{{}_f}=\frac{C_{s,\text{m}\text{e}\text{l}}}{C_{s,\text{m}\text{m}\text{i}\text{s}}}$

$S{G}_m=\frac{{}_m}{{}_f}=\frac{1-C_{s,\text{s}\text{u}\text{l}}}{1-C_{s,\text{m}\text{a}\text{m}}}$

$S{G}_m=\frac{{}_m}{{}_J}=\frac{1-C_{,}}{1-C_{,\text{m}\text{a}\text{d}}}$