If N, m, V, and c represent the number of molecules, the mass of a molecule, the volume of a cubical container, and the speed of a molecule respectively then by using the method dimensions, check which of the following expressions represents the pressure (p) of a gas?

Explanation

The dimensions of pressure can be expressed as force per unit area, or [M L-1 T-2].Using the method of dimensions, we can check which expression has the correct dimensions for pressure.Dimension of N is [M0 L0 T0], m is [M], V is [L3] and c is [L T-1].Putting these values in option A, we get:P = Nm/v2(c2) = [M1 L-1 T-2] which is not the dimension of pressure.Putting these values in option B, we get:P = 3 Nm/v2(c) = [M1 L-1 T-2] which is not the dimension of pressure.Putting these values in option C, we get:P = 3 Nm/v (c2) = [M1 L-1 T-2], which is the correct dimension of pressure.Putting these values in option D, we get:P = 5 Nm2/ v (c2) = [M1 L-1 T-2] which is not the dimension of pressure.Putting these values in option E, we get:P = N2m2/v (c2) = [M1 L-1 T-2] which is not the dimension of pressure.Therefore, the correct answer is C.