Energy is defined as the ability to do work. Work is defined as a force acting through a distance so the basic dimensional units of energy are force x distance. Depending on which measurement system you favor, this could be foot-pounds, Newton-meters, or dyne-centimeters.
Kinetic energy can be defined as the energy possessed by the body by virtue of its motion. Dimensional Formula of Kinetic energy= M1L2T-2. SI unit of Kinetic energy is Joule (J). Note : In the above equation ½ is a constant and constants do not affect the dimensional formula of any quantity.
The stress equation is σ = F/A . F denotes the force acting on a body and A denotes the area. Units of stress are the same as units of pressure - Pascals (symbol: Pa) or Newtons per squared meter.
The dimensions of moment of inertia are always mass times length squared, so all we really had to work out was the factor 1/3.
Dimensional Formula of Frequency = 1/ M0L0T1 = M0L0T-1. Hence, Dimensional Formula of Frequency = M0L0T-1. SI unit of Frequency is the hertz.
Momentum is the the quantity of motion of a moving body, measured as a product of its mass and velocity. p=mv. Therefore the dimensional formula of momentum is. p = [M]x [LT^(-1)] Linear Momentum= MLT^(-1)
The dimensions of viscosity can be determined based on how it is defined. It is defined as the property of a fluid that describe a stress (force/area) per velocity shear rate in the fluid (d velocity/d distance). So the dimensions are (F/A)/(V/L). So the dimensions are (F/A)/(V/L).
It is defined as the ratio of tangential stress to the shearing strain, within the elastic limit. Its unit is N/m2 or Pascal and its dimensional formula is [ML-1T-2]. Compressibility of a material is the reciprocal of its bulk modulus of elasticity. Its SI unit is N-1m2 and CGS unit is dyne-1 cm2.
Stress
- Stress is defined as the force per unit area of a material.
- i.e. Stress = force / cross sectional area:
- Strain is defined as extension per unit length.
- Strain = extension / original length.
- Strain has no units because it is a ratio of lengths.
1 : an act of straining or the condition of being strained: such as. a : bodily injury from excessive tension, effort, or use heart strain especially : one resulting from a wrench or twist and involving undue stretching of muscles or ligaments back strain. b : excessive or difficult exertion or labor.
Young's modulus equation is E = tensile stress/tensile strain = (FL) / (A * change in L), where F is the applied force, L is the initial length, A is the square area, and E is Young's modulus in Pascals (Pa). Using a graph, you can determine whether a material shows elasticity.
Strain is defined as the amount of deformation per unit length of an object when a load is applied. Typical values for strain are less than 0.005 inch/inch and are often expressed in microstrain units: Strain may be compressive or tensile and is typically measured by strain gauges.
Angle is defined as the ratio of length of arc to radius. Substituting in the above formula we get, Dimensional formula of Angle = M0L0T0. We can also say Angle is dimensionless quantity.
In response to stress, rock may undergo three different types of strain – elastic strain, ductile strain, or fracture.
Strain is any change in volume or shape. There are four general
types of stress.
In response to stress, rock may undergo three different types of strain – elastic strain, ductile strain, or fracture.
- Elastic strain is reversible.
- Ductile strain is irreversible.
- Fracture is also called rupture.
Young's modulus = stress/strain = (FL0)/A(Ln − L0). This is a specific form of Hooke's law of elasticity. The units of Young's modulus in the English system are pounds per square inch (psi), and in the metric system newtons per square metre (N/m2).
Pressure is a applied force to the unit area. Its SI unit is Pascal or Newton per metre square. So it's dimensional equation is [ML^-1T^-2] .
The dimension of Planck's constant is the product of energy multiplied by time, a quantity called action. Planck's constant is often defined, therefore, as the elementary quantum of action. Its value in metre-kilogram-second units is defined as exactly 6.62607015 × 10−34 joule second.
In SI units, force is measured in newtons and area in square metres. This means stress is newtons per square meter, or N/m2. However, stress has its own SI unit, called the pascal. 1 pascal (symbol Pa) is equal to 1 N/m2. The dimension of stress is the same as that of pressure.
Magnetic Field = Force × [Charge × Velocity]-1. Or, B = [M1 L1 T-2] × [I1 T1]-1 × [L T-1]-1 = [M1 L0 T-2 I-1]. Therefore, Magnetic Field is dimensionally represented as [M1 T-2 I-1].
Surface tension is the to force per unit length. That means formula for surface tension is = force/length . As we know that the dimensional formula for length is L . And that for force is MLT^-2.
Refractive Index is defined as the relative speed at which light moves through a material with respect to its speed in vacuum. As both the values belong to same quantity (speed), units get nullified. So Refractive Index is dimensionless quantity. Dimensional Formula of Refractive Index = M^0L^0T^0.
