question_answer 67)

                  A new system of units is proposed in which unit of mass is a kg, unit of length b m and unit of time \[\gamma s\]. How much will 5J measure in this new system?                

Answer:

                  \[{{n}_{2}}={{n}_{1}}{{\left[ \frac{{{M}_{1}}}{{{M}_{2}}} \right]}^{a}}{{\left[ \frac{{{L}_{1}}}{{{L}_{2}}} \right]}^{b}}{{\left[ \frac{{{T}_{1}}}{{{T}_{2}}} \right]}^{c}}\]                 \[=5{{\left[ \frac{1\,kg}{\alpha \,kg} \right]}^{1}}{{\left[ \frac{1\,m}{\beta \,m} \right]}^{2}}{{\left[ \frac{1\,s}{\gamma \,s} \right]}^{-2}}\]                 [as dimensional formula for energy is \[[{{M}^{1}}{{L}^{2}}{{T}^{-2}}]\]]                 \[=5\left[ \frac{1}{\alpha } \right]\,{{\left[ \frac{1}{\beta } \right]}^{2}}{{\left[ \frac{1}{\gamma } \right]}^{-2}}=\frac{5{{\gamma }^{2}}}{\alpha {{\beta }^{2}}}\]