The mechanical power delivered to a system is given by the relation P = + F , where and F represent torque and force, respectively. The ratio ( ) has the dimensions of

Step-by-step solution

By the principle of dimensional homogeneity, the terms and F must have the same dimensions. [ ] = [ F] [ ] = [ ] [F] Substituting the dimensional formulas for torque ( [ ] = [ML^2T⁻²] ) and force ( [F] = [MLT⁻²] ): [ ] = [ML^2T⁻²] [MLT⁻²] = [L] The dimension [L] corresponds to length, which is the dimension of radius of gyration. Answer: radius of gyration