The potential energy U of a system as a function of distance x is given by the expression U = A x + B x^2 , where A and B are constants. Which of the following expressions represents a dimensionless quantity?

Step-by-step solution

By the principle of dimensional homogeneity, all terms in a physical equation must have the same dimensions. Therefore, the dimensions of A x and B x^2 must be equal to the dimensions of potential energy U . [ A x ] = [B x^2] [A] [B x^3] = [M^0 L^0 T^0] Thus, the quantity A B x^3 is dimensionless. Answer: A B x^3