The displacement y of an oscillating particle is given by the equation y = a b (1 + b^2 t c ) ( c x a ) , where x is the position, t is the time, and a, b, c are unknown dimensional constants. The physical quantity whose dimensional formula is equivalent to the product ac is :

Step-by-step solution

According to the principle of homogeneity, the arguments of logarithmic and trigonometric functions must be dimensionless. From the argument of the cosine function: [ cx a ] = M ^0 L ^0 T ^0 [c] L [a] = 1 [a] = [c] L From the argument of the logarithmic function: [ b^2 t c ] = M ^0 L ^0 T ^0 [b]^2 T [c] = 1 [c] = [b]^2 T The logarithmic and cosine functions themselves are dimensionless. Therefore, the dimension of y must be equal to the dimension of the prefactor a b : [y] = [ a b ] L = [a] [b] [a] = [b] L Equating