• question_answer Poise is the CGS unit of coefficient of viscosity. Suppose we employ a system of units in which unit of mass is a kg, the unit of length is P metre and unit of time is y s. In this new system, 1Poise is equal to A)  $1000\alpha {{\beta }^{-1}}{{\gamma }^{-1}}$                 B)  $10\alpha {{\beta }^{-1}}{{\gamma }^{-1}}$ C) $0.1{{\alpha }^{-1}}\beta \gamma$                      D)  $0.01{{\alpha }^{-1}}\beta \gamma$

Idea Dimensions of coefficient of viscosity is $[\eta ]=[{{M}^{1}}{{L}^{-1}}{{T}^{-1}}]$ also${{n}_{2}}{{u}_{2}}={{n}_{1}}{{u}_{1}}$ $\Rightarrow$${{n}_{2}}=\frac{{{n}_{1}}{{u}_{1}}}{{{u}_{2}}}$ $={{n}_{1}}{{\left[ \frac{{{M}_{1}}}{{{M}_{2}}} \right]}^{1}}{{\left[ \frac{{{L}_{1}}}{{{L}_{2}}} \right]}^{-1}}{{\left[ \frac{{{T}_{1}}}{{{T}_{2}}} \right]}^{-1}}$ ${{u}_{1}}$and${{u}_{2}}$are two units of measurement and${{n}_{1}}$and${{n}_{2}}$are their respective numerical values. Coefficient of viscosity$\eta =[{{M}^{1}}{{L}^{-1}}{{T}^{-1}}]$ In new system, we have unit of mass $=\alpha \times {{10}^{3}}g$ Unit of length$=\beta \times 100$cm and unit of time = $\gamma$ s So, new system unit is $={{\left[ \frac{1g}{\alpha \times {{10}^{3}}g} \right]}^{1}}{{\left[ \frac{1cm}{100\beta cm} \right]}^{-1}}\left[ \frac{1s}{\gamma s} \right]$ $=0.1{{\alpha }^{-1}}{{\beta }^{-1}}\gamma$ or $=0.1{{\alpha }^{-1}}\beta \gamma$ TEST Edge Every year about 1 to 2 questions are asked from dimension analysis. Besides conversion of one system of units into another, checking of accuracy of formulae and derivation of formulae can also be asked.