Podcast
Questions and Answers
What is the base unit for length in the International System of Units (SI)?
What is the base unit for length in the International System of Units (SI)?
- Kilometer
- Foot
- Centimeter
- Meter (correct)
The kilogram is defined as the mass of a cylinder made of a gold and platinum alloy.
The kilogram is defined as the mass of a cylinder made of a gold and platinum alloy.
False (B)
What is the relationship between the length unit of inch and meter?
What is the relationship between the length unit of inch and meter?
1 inch = 0.0254 m
The standard unit of electric current in the SI system is the ______.
The standard unit of electric current in the SI system is the ______.
Match the quantity with its standard unit in the SI system:
Match the quantity with its standard unit in the SI system:
What is the conversion of 1 mile in meters?
What is the conversion of 1 mile in meters?
The fundamental quantity of luminous intensity is measured in Candela.
The fundamental quantity of luminous intensity is measured in Candela.
How is the second defined in the SI system?
How is the second defined in the SI system?
What is the dimensional formula for velocity?
What is the dimensional formula for velocity?
The dimensions of kinetic energy and potential energy are the same.
The dimensions of kinetic energy and potential energy are the same.
What is the dimension of mass?
What is the dimension of mass?
The formula for distance traveled under constant acceleration is x = _________.
The formula for distance traveled under constant acceleration is x = _________.
Match the following physical quantities with their dimensions:
Match the following physical quantities with their dimensions:
Which of the following represents the dimension of acceleration?
Which of the following represents the dimension of acceleration?
The equation x = k a t^2 cannot determine the constant k using dimensional analysis.
The equation x = k a t^2 cannot determine the constant k using dimensional analysis.
What is the dimension of area?
What is the dimension of area?
What is the SI unit of force?
What is the SI unit of force?
The gravitational constant G has SI units of kg·m/s².
The gravitational constant G has SI units of kg·m/s².
What is represented by the symbols M and m in Newton’s law of universal gravitation?
What is represented by the symbols M and m in Newton’s law of universal gravitation?
The proportionality constant G in Newton’s law has units of _____.
The proportionality constant G in Newton’s law has units of _____.
Which of the following equations is dimensionally correct?
Which of the following equations is dimensionally correct?
What is the primary unit of mass in the SI system?
What is the primary unit of mass in the SI system?
Match the following SI units to their respective physical quantities:
Match the following SI units to their respective physical quantities:
In the equation $F = G \frac{Mm}{r²}$, the variable r represents _____.
In the equation $F = G \frac{Mm}{r²}$, the variable r represents _____.
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Study Notes
International System of Units
- The International System of Units (SI) was established in 1960 by an international committee.
- SI Units define standards for three basic quantities:
- Mass : Kilogram (kg)
- Length : Meter (m)
- Time : Second (s)
Other Quantities
- Other quantities defined by the SI include:
- Electric current : Ampere (Amp)
- Temperature : Kelvin (K)
- Luminous intensity : Candela
- Amount of substances : mol
Other Systems of Units
- The CGS system uses centimeter (cm) for length, gram (gm) for mass, and second (s) for time.
- The MKS system uses meter (m) for length, kilogram (kg) for mass and second (s) for time.
- The British Engineering System uses Foot (ft) for length, Pound (lb) for mass, and second (s) for time.
Conversion of Units
- Units can be converted between systems.
- For example:
- 1 mile = 1609 m = 1.609 km
- 1 ft = 0.3048 m = 30.48 cm
- 1 inch = 0.0254 m = 2.54 cm
- 1 m = 100 cm
- 1 kg = 1000 gm
Dimensional Analysis
- Dimension refers to the physical nature of a quantity.
- Basic dimensions in mechanics are:
- Length (L)
- Mass (M)
- Time (T)
Dimensions of Physics Quantities
- Dimensions of some common physics quantities include:
- Area: [A] = L.L = L²
- Volume: [V] = L.L.L = L³
- Velocity: [ν] = L / T = LT⁻¹
- Acceleration: [a] = L / T² = LT⁻²
- Momentum: [P] = [m].[ν] = MLT⁻¹
- Kinetic Energy: [K.E] = [1/2].[m].[ν²] = M((LT⁻¹)²) = ML²T⁻²
- Potential Energy: [P.E] = [m].[g].[h] = M(LT⁻²) L = ML²T⁻²
Dimensional Analysis Applications
- Dimensional analysis can be used to:
- Check the validity of a formula
- Derive some formulas
Example 2 : Deriving Formula for Distance Traveled
- Derive formula for distance (x) traveled by a car starting from rest with constant acceleration (a).
- We assume distance is dependent on time (t) and acceleration (a): x α tⁿ aᵐ
- Applying dimensional analysis:
- = L
- [tⁿaᵐ] = Tⁿ (LT⁻²)ᵐ = LᵐTⁿ⁻²ᵐ
- Matching dimensions:
- L = LᵐTⁿ⁻²ᵐ
- Solving for m and n:
- n-2m = 0
- m = 1
- n = 2
- Therefore, x α t² a¹ or x = k at² (where k is a constant)
Example 3 : Analyzing a Power Law
- Determine power of radius (r) and velocity (v) to express centripetal acceleration (a) for an object moving in a circular orbit.
- Assume a α rⁿ vᵐ.
- Applying dimensional analysis:
- [a] = LT⁻²
- [rⁿvᵐ] = Lⁿ (LT⁻¹)ᵐ = Lⁿ⁺ᵐT⁻ᵐ
- Solving for n and m:
- n + m = 1
- -m = -2
- m = 2
- n = -1
- Therefore, a α r⁻¹v².
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