Question

A metal box is made up of an alloy of zinc and copper metals. It weighs 20 g and 520 g in a liquid of R .D of 1.4 and water, respectively. The specific gravities of zinc and copper are 7.4 and 8.9, respectively. Arrange the following steps in a proper sequential order to find the masses of metals in the alloy.

(A) Find the weight of the box in a liquid of relative density 1.4 and water along with relative densities of zinc and copper from the given data.
(B) Note down the metals present in the metal box
(c) The relative density of liquid $1.4=\frac{\mathrm{W}-20}{\mathrm{W}-320}$. Find the value of W.

(D) Let the masses and volumes of copper and zinc be ${\mathrm{m}}_{\mathrm{c}}\mathrm{and}{\mathrm{m}}_{\mathrm{z}}$
,${\mathrm{V}}_{\mathrm{c}}\mathrm{and}{\mathrm{V}}_{\mathrm{z}}\mathrm{respectively}\mathrm{weight}\mathrm{and}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{box}\mathrm{respectively}\mathrm{are}({\mathrm{m}}_{\mathrm{z}}+{\mathrm{m}}_{\mathrm{c}})\mathrm{and}({\mathrm{v}}_{\mathrm{z}}+{\mathrm{v}}_{\mathrm{c}})\mathrm{respectivley}.$

(E) substitute $V_c=\frac{m_c}{d_c}and{V}_z=\frac{m_z}{d_z}=\left(\frac{W-m_c}{d_z}\right)tofindthemassesof{m}_{c}and{m}_z$

(F) $\mathrm{the}\mathrm{density}\mathrm{of}\mathrm{alloy}\mathrm{d}=\frac{\mathrm{W}}{\mathrm{W}-320}$

• A. BADCFE
• B. BCDAFE
• C. ABDCEF
• D. ABCDEF

Answer 1

The correct option is A

BADCFE

$$\begin{gathered} \mathrm{First}\mathrm{note}\mathrm{down}\mathrm{the}\mathrm{metals}\mathrm{present}\mathrm{in}\mathrm{the}\mathrm{box}--\left(\mathrm{B}\right) \\ \mathrm{the}\mathrm{weight}\mathrm{of}\mathrm{the}\mathrm{box}\mathrm{in}\mathrm{a}\mathrm{liquid}\mathrm{having}\mathrm{relative}\mathrm{density}1.4\mathrm{is}\mathrm{found}\mathrm{out};\mathrm{here}\mathrm{the}\mathrm{relative}\mathrm{density}\mathrm{of}\mathrm{zinc}\mathrm{and}\mathrm{copper}\mathrm{is}\mathrm{also}\mathrm{found}\mathrm{out}\mathrm{as}\mathrm{specific}\mathrm{gravity}\mathrm{of}\mathrm{them}\mathrm{are}\mathrm{given}---\left(\mathrm{A}\right) \\ \mathrm{Before}\mathrm{finding}\mathrm{the}\mathrm{weight}\mathrm{let}\mathrm{masses}\mathrm{of}\mathrm{copper}\mathrm{and}\mathrm{zinc}\mathrm{be}\mathrm{considered}\mathrm{as}{\mathrm{m}}_{\mathrm{c}},{\mathrm{m}}_{\mathrm{z}}\mathrm{with}\mathrm{their}\mathrm{volumes}{\mathrm{V}}_{\mathrm{c}}\mathrm{and}{\mathrm{V}}_{\mathrm{z}}\mathrm{respectivley} \\ \mathrm{and}\mathrm{the}\mathrm{weight}\mathrm{of}\mathrm{the}\mathrm{box}=({\mathrm{m}}_{\mathrm{c}}+{\mathrm{m}}_{\mathrm{z}});\mathrm{its}\mathrm{volume}=({\mathrm{V}}_{\mathrm{c}}+{\mathrm{V}}_{\mathrm{z}})---\left(\mathrm{D}\right) \\ \mathrm{The}\mathrm{weight}\mathrm{of}\mathrm{the}\mathrm{liquid}\mathrm{is}\mathrm{found}\mathrm{out}\mathrm{by}\mathrm{substitutint}\mathrm{the}\mathrm{relative}\mathrm{density}(\mathrm{i}.\mathrm{e})1.4=\frac{\mathrm{W}-20}{\mathrm{W}-320} \\ \mathrm{Inorder}\mathrm{to}\mathrm{find}\mathrm{the}\mathrm{masses}\mathrm{we}\mathrm{need}\mathrm{to}\mathrm{find}\mathrm{the}\mathrm{density}\mathrm{of}\mathrm{the}\mathrm{alloy}=\frac{\mathrm{W}}{\mathrm{W}-320}\mathrm{and}\mathrm{the}\mathrm{individual}\mathrm{component}\text{'}\mathrm{s}\mathrm{density}\mathrm{can}\mathrm{be}\mathrm{found}\mathrm{out}\mathrm{using}\mathrm{specific}\mathrm{gravity}\mathrm{given}---\left(\mathrm{F}\right) \\ \mathrm{the}\mathrm{densities}\mathrm{of}\mathrm{the}\mathrm{copper}\mathrm{and}\mathrm{zinc}\mathrm{along}\mathrm{with}\mathrm{its}\mathrm{volume}\mathrm{can}\mathrm{be}\mathrm{used}\mathrm{to}\mathrm{find}\mathrm{their}\mathrm{mass}\mathrm{by}\mathrm{susbstituting}\mathrm{in} \\ {\mathrm{V}}_{\mathrm{c}}=\frac{{\mathrm{m}}_{\mathrm{c}}}{{\mathrm{d}}_{\mathrm{c}}}\mathrm{and}{\mathrm{V}}_{\mathrm{z}}=\frac{{\mathrm{m}}_{\mathrm{z}}}{{\mathrm{d}}_{\mathrm{z}}}=\left(\frac{\mathrm{W}-{\mathrm{m}}_{\mathrm{c}}}{{\mathrm{d}}_{\mathrm{z}}}\right)\mathrm{where}\mathrm{d}\mathrm{is}\mathrm{the}\mathrm{density}\mathrm{of}\mathrm{substances}.---\left(\mathrm{E}\right) \\ \mathrm{Thus}\mathrm{the}\mathrm{sequential}\mathrm{order}\mathrm{is}\mathrm{BADCFE}.\mathrm{option}\left(\mathrm{a}\right)\mathrm{is}\mathrm{the}\mathrm{correct}\mathrm{answer}. \end{gathered}$$