What are the basic rules of dimensional analysis?
1) two physical quantities can only be equated if they have the same dimensions 2) two physical quantities can only be added if they have the same dimensions 3) the dimensions of the multiplication of two quantities is given by the multiplication of the dimensions of the two quantities.
What are the two methods of dimensional analysis?
The following two methods are important to develop the relationship between physical quantities. Rayleigh’s method. Buckingham’s pi-theorem.
What is the dimensional formula of time?
The dimensional formula of the time period is given by [M0L0T1]. Or, T = √[M0 L1 T0] × [M0 L1 T-2]-1 = √[T2] = [M0 L0 T1]. Therefore, the time period is dimensionally represented as [M0 L0 T1].
What is dimensional formula give an example?
A formula that represents a physical quantity in terms of fundamental units along with appropriate dimensions within parenthesis or square bracket is known as a dimensional formula. e.g., : Dimensional formula for force is (M1L1T-2) .
What are the uses dimensional formula?
Dimensional equations are used : To check the correctness of an equation. To derive the relation between different physical quantities. To convert one system of units into another system.
What is the difference between dimensional formula and dimensional equation?
Dimensional Formula is the expression which shows how and which of the base quantities represent the dimensions of a physical quantity. Dimensional Equation is an equation obtained by equating a physical quantity with its dimensional formula.
What are the advantages of dimensional formula?
There are following uses or advantages of dimensional analysis.
- To check the correctness of a given relation.
- To derive the relationship between various physical quantities.
- To determine the dimensions of unknown quantities.
- Conversion of one system of units into the other system of units. Answer verified by Toppr.
What is the dimensional formula of mass?
What is the dimensional formula of mass per unit length? S = 2πr (r + h).
What is the dimensional formula of stress?
Therefore, stress is dimensionally represented as [M1 L-1 T-2].
What is SI unit of stress?
SI unit – Nm2or Pascal (Pa) Dimension of stress: Stress = ForceArea=MLT−2L2Stress=ML−1T−2. Strain is defined as the response of a system to an applied stress. When a substance or a material is loaded with a force, it produces a stress, which then causes that material to deform.
What is strain formula?
Strain is simply the measure of how much an object is stretched or deformed. Strain occurs when force is applied to an object. Strain = Δ L L = Change in Length Original Length . \text{Strain}=\dfrac{\Delta L}{L}=\dfrac{\text{Change in Length}}{\text{Original Length}}. Strain=LΔL=Original LengthChange in Length.
What is dimensional formula of force?
Dimensional formula of force is = [M1 L1 T-2] Dimensional equation of force is [force] = [M1 L1 T-2] As discussed above you can find the dimensions of any given physical quantities.
What is the dimensional formula of distance?
Dimensional Formula of Distance= M0L1T0. Dimensional Formula of Time= M0L0T1. SI unit of Distance traveled in nth second is ms-1.