Two heavy rotating masses are connected by shafts of lengths $${l_1},\,{l_2}$$ �

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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

Options:

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

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