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From the moment of inertia of C2H2 and C2D2, I have to calculate the C≡C and C-H (C-D) bond lengths. I am confused on how to form the 2 simultaneous equations.
What is the moment of inertia for a collection of point particles in general? Does this match what you have written?
Edit: my apologies. I see from the picture in OP how you have defined ##r_H## and ##r_C##. Your moment of inertia equations are correct. What is the next step?