The force F acting on a particle is given by the relation F = A (B t) + C x^2 , where t represents time and x represents distance. If A , B , and C are dimensional constants, what is the dimensional formula of the quantity AB C ?

Step-by-step solution

According to the principle of dimensional homogeneity, each term added together must have the same dimensions, and the argument of a trigonometric function must be dimensionless. The dimension of force is [F] = [MLT⁻²] . For the first term, A (Bt) must have the dimensions of force. Since the sine function itself is dimensionless, we have: [A] = [F] = [MLT⁻²] The argument of the sine function, Bt , must be dimensionless: [Bt] = 1 [B] = 1 [t] = [T⁻¹] For the second term, C x^2 must also have the dimensions of force: