If pressure [P] , velocity [V] and time [T] are chosen as the fundamental physical quantities, what will be the dimensional formula of force?

Step-by-step solution

Let [Force] = [P]^a [V]^b [T]^c Substituting the standard dimensional formulas for each quantity: [MLT⁻²] = [ML⁻¹T⁻²]^a [LT⁻¹]^b [T]^c [MLT⁻²] = [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 = 1 -1 + b = 1 b = 2 For T : -2a - b + c = -2 -2(1) - 2 + c = -2 -4 + c = -2 c = 2 Therefore, the dimensional formula of force in this new system is [P][V]^2[T]^2 . Answer: [P][V]^2[T]^2