Dimension for pressure how to proof it
Answers
Answer:
The dimensional formula of pressure is given by,
M1 L-1 T-2
Where,
M = Mass
L = Length
T = Time
Derivation
Pressure (P) = Force × Area-1 . . . . . (1)
Since, Force = Mass × Acceleration
And, acceleration = velocity × time-1 = [L T-1] [T]-1 = [L T-2]
∴ The dimensional formula of force = [M] × [L T-2] = Force = M1 L1 T-2 . . . . (2)
The dimensional formula of area = M0 L2 T0 . . . . (3)
On substituting equation (2) and (3) in equation (1) we get,
Pressure (P) = Force × Area-1
Or, P = [M1 L1 T-2] × [L2]-1 = M1 L-1 T -2.
Therefore, the pressure is dimensionally represented as M1 L-1 T -2.
hope it helps ❤️
Explanation:
Dimensional Formulae of Length = [L], Time = [T], Mass = [M]
Pressure, p = Force/Area - - - - - - - - (1)
Force, F = mass × acceleration—————(2)
Acceleration, a = initial velocity- final velocity/ time - - - - - - - - (3)
Velocity, v = displacement/time
V = [L] /[T]
V = [LT^-1] - - - - - - - - (4)
Putting (4) in (3)
Acceleration, a = [LT^-1] - [LT^-1] /[T]
a = [LT^-1] /[T]
a = [LT^-2] - - - - - - - (5)
Putting (5) in (2)
Force, F = [M] × [LT^-2]
F = [MLT^-2] –———————(6)
Putting (6) in (1)
Pressure, p = [MLT^-2]/ [L^2]
Pressure, p = [ML^-1T^-2]