Derive the dimensional formula for pressure and work done
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DIMENSIONAL FORMULA
Quantity Relation with other quantities Dimensional form
Quantity Relation with other quantities Dimensional form
pratheeksha47:
Work Force × Distance L2 MT-2
Pressure Force/area L -1MT-2
Angle Arc/radius L0 M0 T0
Angular, velocity Angular/time L0 M0 T-1
Period Time L0 M0 T
Frequency No. of vibration/time L0 M0 T-1
Stress Force/area L-1 MT-2
Strain Change in length/length L0 M0 T0
Elasticity Stress/strain L-1 MT-2
Surface Tension Force/length L0 MT-2
Viscosity Pressure/velocity gradient L-1 MT-1
Angle Arc/radius L0 M0 T0
Angular, velocity Angular/time L0 M0 T-1
Period Time L0 M0 T
Frequency No. of vibration/time L0 M0 T-1
Stress Force/area L-1 MT-2
Strain Change in length/length L0 M0 T0
Elasticity Stress/strain L-1 MT-2
Surface Tension Force/length L0 MT-2
Viscosity Pressure/velocity gradient L-1 MT-1
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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]
Concept—SI base unit
Mass—kg
Displacement—m
Time—s
—
Work = Force x Displacement | J = N•m
Force (N) = Mass x Acceleration
Acceleration = m•s^2
Work = Mass x Acceleration x Displacement
Work in base SI units = kg•m/s^2•m =
kg•m^2/s^2
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]
Concept—SI base unit
Mass—kg
Displacement—m
Time—s
—
Work = Force x Displacement | J = N•m
Force (N) = Mass x Acceleration
Acceleration = m•s^2
Work = Mass x Acceleration x Displacement
Work in base SI units = kg•m/s^2•m =
kg•m^2/s^2
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