question_answer

A solid sphere of volume V and density p floats at the interface of two immiscible liquids of densities \[{{p}_{1}}\]and \[{{p}_{2}}\]respectively. If  \[{{p}_{1}}<p<{{r}_{2}}\]then the ratio of volume of the parts of the sphere in upper and lower liquids is:

A) \[\frac{p-{{p}_{1}}}{{{p}_{2}}-p}\]

B)               \[\frac{{{p}_{2}}-p}{p-{{p}_{1}}}\]

C) \[\frac{p+p}{p+{{p}_{2}}}\]               

D) \[\sqrt{\frac{{{p}_{1}}{{p}_{2}}}{p}}\]

Correct Answer: B

Solution :

[b] \[V\,pg={{V}_{1}}{{p}_{1}}+{{V}_{2}}{{p}_{2}}g\,\therefore \,V={{V}_{1}}+{{V}_{2}}\] \[({{V}_{1}}+{{V}_{2}})\,pg={{V}_{1}}{{p}_{1}}+{{V}_{2}}{{p}_{2}}g\] \[{{V}_{1}}pg+{{V}_{2}}pg={{V}_{1}}{{p}_{1}}g+{{V}_{2}}{{p}_{2}}g\] \[{{V}_{1}}+{{V}_{2}}p={{V}_{1}}{{p}_{1}}+{{V}_{2}}{{p}_{2}}\] \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{{{P}_{2}}-P}{p-{{p}_{1}}}\]