Question

b) Check the dimensional
correctness of the equation
PV = Fx where P is the
pressure, V is volume, F is
force and x is displacement.​

Answer 1

Answer:

Yes, The equation is dimensionally correct.

Explanation:

Dimensional formulae of the terms on the left hand side

Pressure = Force / Area

$P = ML^{-1}T^{-2} \\ </p><p>$

Volume = Area × Length

$V = L^3 \:$

Dimensional formulae of the terms on the right hand side

Force = mass × Acceleration

$F = MLT^{-2} \:$

Displacement :

$x = L$

Now,

$\boxed {\mathbb{P.V = Fx}}$

$ML^{-1}T^{-2} \times L^3 = MLT^{-2} \times L \\ \\ ML^{2} T^{-2} = ML^2T^{-2} \:$

Since the dimensions on both sides are equal, The given equation is dimensionally correct.

Answer 2

Answer:

[MLT-2][LT-1]

P×v=[ML-1T-2][L3]