Question

Check dimensional consistency of
*fx=p×v*

Answer 1

The complete question is:

Check the dimensional  correctness of the equation

PV = Fx

where P is the  pressure, V is volume, F is  force and x is displacement.​

Solution:

For the terms on the left hand side , we know that:

Pressure = Force / Area  = [M L-1 T-2]

Volume = Area × Length = [M0 L³ T0]

So PV = [M L²T-2]

For the terms on the right hand side , we know that:

Force = mass × Acceleration  = [M L T-2]

Displacement x = [M0 L T0]

Force× Displacement = Fx = [M L² T-2]

Therefore the equation is dimensionally correct.