The velocity of a body moving in a viscous medium is given by v = A B+C [1 - e^ -t B ] where t is time; dimensions of A and C are

Step-by-step solution

The exponent of an exponential function must be dimensionless. Therefore, the dimension of t B is [M^0L^0T^0] . [B] = [t] = [M^0L^0T^1] By the principle of homogeneity, quantities added or subtracted must have the same dimensions. Since B and C are added in the denominator, [C] = [B] = [M^0L^0T^1] . The term [1 - e^ -t B ] is dimensionless. Thus, the dimensions of velocity v must equal the dimensions of A B+C . [v] = [A] [B+C] [M^0L^1T⁻¹] = [A] [M^0L^0T^1] [A] = [M^0L^1T⁻¹] [M^0L^0T^1] = [M^0L^1T^0] The dimensions