Two heavy rotating masses are connected by shafts of lengths $${l_1},\,{l_2}$$  and $${l_3}$$ and the corresponding diameters are d₁, d₂ and d₃. This system is reduced to a torsionally equivalent system having uniform diameter d = d₁ of the shaft. The equivalent length of the shaft is

A. $$\frac{{{l_1} + {l_2} + {l_3}}}{3}$$

B. $${l_1} + {l_2}{\left( {\frac{{{{\text{d}}_1}}}{{{{\text{d}}_2}}}} \right)^3} + {l_3}{\left( {\frac{{{{\text{d}}_1}}}{{{{\text{d}}_3}}}} \right)^3}$$

C. $${l_1} + {l_2}{\left( {\frac{{{{\text{d}}_1}}}{{{{\text{d}}_2}}}} \right)^4} + {l_3}{\left( {\frac{{{{\text{d}}_1}}}{{{{\text{d}}_3}}}} \right)^4}$$

D. $${l_1} + {l_2} + {l_3}$$

Answer: Option C