The ratio of the internal forces to the external forces will depend upon its speed, and the viscosity of the fluid, and the size of the body. But the ratio of the internal to the viscous forces is dimensionless , so it must depend on some combination of the viscosity, speed V and linear size l that is dimensionless.
Which is not a dimensionless quantity?
The dimensional formula of moment of inertia is [ML2T0]. This means that angular momentum is not a dimensionless quantity. Therefore, no given quantities are dimensionless. So, the correct answer is “Option D”.
Which physical quantities are dimensionless?
All pure numbers are dimensionless quantities, for example 1, i, π, e, and φ. Units of number such as the dozen, gross, googol, and Avogadro’s number may also be considered dimensionless. Coefficient of friction , refractive index are also dimensionless.
Is weight a dimensionless quantity?
Specific Gravity is a dimensionless number equivalent to relative density and is relative to water at a specific set of conditions; thus we divide the weight of any volume of a substance by the weight of the same volume of water.
Which is dimensionless quantity?
In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned , also known as a bare, pure, or scalar quantity or a quantity of dimension one, with a corresponding unit of measurement in the SI of the unit one (or 1), which is not explicitly shown.
Is there any Unitless quantity?
A substance can have a unit even if it doesn’t have a dimension. But the reverse is not true. ... So dimensionless physical quantities can have units. When considering unitless quantities it is impossible for them to have any dimension , since a unitless quantity does not have dimensions.
Is stress dimensionless quantity?
$dimensionless. Hint: We can define stress as the reactive force per unit area . Mathematically it is defined as the ratio of force and area of cross-section. Keeping the characteristics of stress in mind we will find the correct option.
Is refractive index is dimensionless quantity?
Since the speed of light in vacuum and the speed of light in different mediums have the same dimensions, a quantity which is the ratio of these two will be dimensionless. ... So, we can say that the refractive index is a dimensionless quantity .
Is specific gravity dimensionless?
For example, liquid mercury has a density of 13.6 kg per litre; therefore, its specific gravity is 13.6. ... Because it is the ratio of two quantities that have the same dimensions (mass per unit volume), specific gravity has no dimension .
Is angle a dimensionless quantity?
Angles. Angles play an essential role in mathematics, physics, and engineering. ... For example, in the current SI, it is stated that angles are dimensionless based on the definition that an angle in radians is arc length divided by radius, so the unit is surmised to be a derived unit of one, or a dimensionless unit.
Is Young’s modulus dimensionless?
It is a dimensionless quantity . So, the units of young’s modulus will be the same as that of stress developed.
Can a quantity have units and still be dimensionless?
The answer is Yes, There are such unit quantities, but dimensional quantities . Note: The dimension quantity with one as a quantity that is not associated with any physical dimension. ... In Maths and Physics, these dimensionless quantities are regularly used.
What are the basic physical quantities?
- Length.
- Mass.
- Time.
- Electric current.
- Temperature.
- Amount of substance.
- Luminous Intensity.
- Plane angle.
Is specific heat a dimensionless quantity?
Like specific gravity, specific heat is a dimensionless quantity , i.e., a pure number having no unit of measurement associated with it.
Is Reynolds number dimensionless?
The Reynolds number is a dimensionless number . High values of the parameter (on the order of 10 million) indicate that viscous forces are small and the flow is essentially inviscid. The Euler equations can then be used to model the flow.
What is dimensionless time?
The “dimensionless time” is just a way of scaling the time coordinate in relation to the mass of the hole . Some sources also use a dimensionless radial coordinate which is constructed basically the same way, as a ratio of the usual radial coordinate to a constant times the hole’s mass.
