An unknown physical quantity Y is defined by the equation Y = ( ) ( t mx ) , where t is time, x is distance, and m is mass. If the dimensional formula of the constant is given as [L⁻¹T^2] , which of the following physical quantities does Y represent?

Step-by-step solution

The argument of any trigonometric function must be a dimensionless quantity. Therefore, the dimension of t mx must be 1 (dimensionless). [ t mx ] = 1 [ ] = [m][x] [t] = [M][L] [T] = [MLT⁻¹] The equation for Y is Y = ( ) ( t mx ) . Since the cosine term is dimensionless, the dimensions of Y are simply the dimensions of . Given that [ ] = [L⁻¹T^2] , we can substitute this to find [Y] : [Y] = [ ] [ ] = [MLT⁻¹] [L⁻¹T^2] [Y] = [M L^ 1 - (-1) T^ -1 - 2 ] = [ML^2T⁻³] The dimensional formula [ML^2T⁻³] corresponds to Power