Podcast Beta
Questions and Answers
What is the base unit for length in the International System of Units (SI)?
The kilogram is defined as the mass of a cylinder made of a gold and platinum alloy.
False
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 ______.
Signup and view all the answers
Match the quantity with its standard unit in the SI system:
Signup and view all the answers
What is the conversion of 1 mile in meters?
Signup and view all the answers
The fundamental quantity of luminous intensity is measured in Candela.
Signup and view all the answers
How is the second defined in the SI system?
Signup and view all the answers
What is the dimensional formula for velocity?
Signup and view all the answers
The dimensions of kinetic energy and potential energy are the same.
Signup and view all the answers
What is the dimension of mass?
Signup and view all the answers
The formula for distance traveled under constant acceleration is x = _________.
Signup and view all the answers
Match the following physical quantities with their dimensions:
Signup and view all the answers
Which of the following represents the dimension of acceleration?
Signup and view all the answers
The equation x = k a t^2 cannot determine the constant k using dimensional analysis.
Signup and view all the answers
What is the dimension of area?
Signup and view all the answers
What is the SI unit of force?
Signup and view all the answers
The gravitational constant G has SI units of kg·m/s².
Signup and view all the answers
What is represented by the symbols M and m in Newton’s law of universal gravitation?
Signup and view all the answers
The proportionality constant G in Newton’s law has units of _____.
Signup and view all the answers
Which of the following equations is dimensionally correct?
Signup and view all the answers
What is the primary unit of mass in the SI system?
Signup and view all the answers
Match the following SI units to their respective physical quantities:
Signup and view all the answers
In the equation $F = G \frac{Mm}{r²}$, the variable r represents _____.
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Test your knowledge of the International System of Units (SI) and its significance in defining mass, length, and time. This quiz also covers other unit systems like CGS and MKS, and the conversion between units. Challenge yourself and see how well you understand the basics of measurement!
