If pressure P , velocity V , and time T are taken as the fundamental physical quantities, the dimensional formula of mass would be:

Step-by-step solution

Let the dimensional formula of mass in terms of the new fundamental quantities be: [M] = [P]^a [V]^b [T]^c The dimensions of the given physical quantities in terms of mass ( M ), length ( L ), and time ( T ) are: Pressure, [P] = Force Area = [M L⁻¹ T⁻²] Velocity, [V] = [L T⁻¹] Time, [T] = [T] Substituting these dimensions into the assumed equation: [M^1 L^0 T^0] = [M L⁻¹ T⁻²]^a [L T⁻¹]^b [T]^c [M^1 L^0 T^0] = [M^a L^ -a+b T^ -2a-b+c ] Comparing the powers of M , L , and T on both sides: For M : a = 1 For L : -a + b