What is Dimensional Formula of Energy density ?

Energy Density is defined as the amount of energy stored in system or region of space per unit volume.

Mathematically,

Energy Density = Energy / Volume.

Dimensional Formula of Energy = M1L2T-2
Dimensional Formula of Volume= M0L3T0

Putting these values in the given equation we get,

Dimensional Formula of Energy Density=M1L-1T-2
SI unit of Energy Density is  J m-3 (Joule per cubic meter)

What is Dimensional Formula of Escape velocity ?

Escape velocity is defined as minimum velocity required to escape from the gravitational pull of the earth.

Mathematically,

Escape velocity (Ve) =  ( 2 G M / r) 1/2 where

G = Universal Gravitational constant

M = Mass of earth in kg

r= distance to center of earth in meters

Dimensional Formula of Universal Gravitational constant = M-1L3T-2
Dimensional Formula of Mass of earth = M1L0T0
Dimensional Formula of distance to center of earth = M0L1T0

Putting these values in above equation we get,

Ve = ( [M-1L3T-2] [M1L0T0] / [M0L1T0] ) 1/2

Ve = (M0L2T-2) 1/2

Ve = M0L1T-1

Dimensional Formula of Escape velocity (Ve) = M0L1T-1
SI Unit of Escape velocity(Ve) is ms-1

What is Dimensional Formula of Critical velocity ?

Critical velocity is defined as the maximum velocity of a fluid above which a streamline flow changes to turbulent flow. In other words critical velocity the maximum velocity of fluid upto which its flow remains streamline and if the velocity of a fluid increases more than its critical velocity the flow of fluid becomes turbulent.

Mathematically,

Critical velocity (VC) = Re   η /  ρ  r    

where

Re = Reynolds number

η = coefficient of viscosity

ρ = density of fluid

r = radius of tube.
Dimensional Formula of Reynolds number (Re) = M0L0T0
Dimensional Formula of coefficient of viscosity (η) =  M1L-1T-1
Dimensional Formula of Density of fluid (ρ) =M1L-3T0
Dimensional Formula of radius (r) = M0L1T0

Putting these values in above equation we get,

VC = [M0L0T0] [M1L-1T-1] / [M1L-3T0] [M0L1T0]

Dimensional Formula of Critical velocity(VC) = M0L1T-1
SI unit of Critical velocity(VC) is ms-1

What is Dimensional Formula of moment of couple?

Moment of couple is defined as the product of perpendicular distance between the forces and magnitude of the force.

Mathematically,

Moment of couple = Force x Distance

Dimensional Formula of Force= M1L1T-2
Dimensional Formula of Distance = M0L1T0

Putting these values in the given equation we get,

Dimensional Formula of moment of couple = M1L2T-2
SI unit of moment of couple is Newton metre (N m)

What is Dimensional Formula of moment of force?

The moment of force is defined as the tendency to produce rotation of object on its axis.

Mathematically,

Moment of force=Force x Distance

Dimensional Formula of Force= M1L1T-2
Dimensional Formula of Distance = M0L1T0

Putting these values in the given equation we get,

Dimensional Formula of moment of force = M1L2T-2
Si unit of moment of force is Newton metre (N m)

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