Physics Chapter: Units and Dimensions

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Questions and Answers

What is the SI base unit for length?

millimeter

centimeter

kilometer

meter (correct)

Which of the following represents the dimension of force?

[MLT^-2] (correct)

[MLT]

[MLT^2]

[MLT^-1]

What does the principle of homogeneity state about dimensions in equations?

Dimensions can be ignored in mathematical equations.

Both sides of an equation must have the same dimension. (correct)

Dimensions have no impact on the correctness of equations.

All equations are dimensionally correct.

How do you calculate mean absolute error when true value is not known?

Use the arithmetic mean of all values. Signup and view all the answers

Which physical quantity is represented by the dimension [ML^2T^-2]?

Work Signup and view all the answers

What is a dimensionless quantity according to the content?

Radian Signup and view all the answers

What is the formula for relative error?

Δa/a Signup and view all the answers

What kind of quantities can have dimensional representation?

All physical quantities Signup and view all the answers

What is the formula to calculate percentage error?

Relative error * 100 Signup and view all the answers

In the propagation of error when adding two measurements, what is the correct expression for the absolute error in the result?

±(ΔX + ΔY) Signup and view all the answers

How is the total reading of a Vernier caliper calculated?

Main scale reading + Vernier scale reading - zero error Signup and view all the answers

What does the least count (LC) of a measuring instrument represent?

The smallest division on the scale Signup and view all the answers

In the screw gauge measurement, what indicates that there is no zero error?

Main scale zero coincides with the reference line Signup and view all the answers

What does the formula Δx/x = ± (Δp/p + Δq/q + Δr/r + Δs/s + Δg/g + Δh/h) represent?

Propagation of error in multiplication/division Signup and view all the answers

Which of the following equations represents the error calculation caused by zero error in a Vernier or screw gauge?

Error = C.V.S.D x L.C. Signup and view all the answers

When taking a reading on a Vernier Caliper, if there is a positive zero error, how is it corrected?

Subtracting zero error from the reading Signup and view all the answers

Study Notes

Unit and Dimension

Units: Standard of representing physical quantities.
- CGS system:
  - Mass: gram (g) = 1 kg
  - Length: centimeter (cm) = 1 m
  - Time: second (s)
- MKS system:
  - Mass: kilogram (kg) = 10³ g
  - Length: meter (m) = 10² cm
  - Time: second (s)
Physical quantity:
- PQ = Numerical value x Unit
- Constant (B) = Numerical value (n) x Unit (y)
- Changing the unit (y) changes the numerical value (n) but the physical quantity (Q) remains constant.
Dimension: The power of M (mass), L (length), and T (time) needed to represent any physical quantity.
- Velocity: [v] = [MLT^-1]
- Acceleration: [a] = [MLT^-2]
- Force: [F] = [MLT^-2]
- Pressure/Stress: [p] = [ML^-1T^-2]
- Work/Energy/Torque: [W] = [ML²T^-2]
- Power: [P] = [ML²T^-3]
- Angular momentum: [L] = [ML²T^-1]
- Impulse: [J] = [MLT^-1]
- Planck's constant: [h] = [ML²T^-1]
- Gravitational constant: [G] = [ML³T^-2]
- NOTE: Dimensions of any physical quantity do not depend on the formula used for calculation.

Dimension Rules

Rule 1: The dimension of a quantity must be consistent with the physical quantity it represents.
- Example: Pressure - x (some quantity) → x must be a kind of pressure.
Rule 2: Dimension of the Left Hand Side (LHS) must be equal to the Dimension of the Right Hand Side (RHS).
- Principle of Homogeneity: An equation can be dimensionally correct but not mathematically correct.
  - If an equation is mathematically correct, it will also be dimensionally correct, with some exceptions.
  - Example: Dimensional correctness doesn't guarantee mathematical correctness.

Other

Dimensionless Quantities:
- Angle (θ): Dimensionless but has unit (radian).
- Trigonometric functions: sin θ, cos θ are dimensionless.
- Logarithmic functions: log(...) are dimensionless.
- Exponential functions: e(...) are dimensionless.
Constant Values: Q = ny = constant
- Example: D1/4/1 = D2/4/2
- This implies that the product of the numerical value (n) and the unit (y) is constant, even if either n or y changes.
Error Analysis:
- Absolute error: True value - Measured value
- Mean absolute error: Δam = Δa1 + Δa2 + Δa3 +....n
 - When the true value is not given, the mean value is used as the true value.
- Relative error: Δa/a or Δam/am
- Percentage error: Relative error * 100.
Propagation of error in addition/subtraction and multiplication/division:
- Addition/Subtraction:
  - X = x + x, Y = y + y, Z = X + Y or Z = X - Y
  - ΔZ = ± (ΔX + ΔY)
- Multiplication/Division:
  - Z = X · Y or Z = X / Y
  - ΔZ = ± (ΔX / X + ΔY / Y)
Propagation of error in general:
- If any physical quantity (x) is represented as x = ap bq cr ds/egfh
- Δx/x = ± (Δp/p + &916;q/q + Δr/r + Δs/s + Δg/g + Δh/h)

Measuring Instruments: Vernier Caliper

Total reading: Main scale reading (MSR) + Vernier scale reading (VSR) - Zero error
- Main scale reading: Mark on the main scale just before the zero of the Vernier scale.
- Vernier scale reading: Coinciding division of Vernier scale with any main scale mark.
Least count (LC):
- LC = IMSD - IVSD
- LC = x (1 - IMSD / IVSD)
  - IMSD = Interval on main scale division
  - IVSD = Interval on Vernier scale division
Zero error:
- No zero error: The zero of the Vernier scale coincides with the zero of the main scale.
- Positive zero error: The zero mark on the Vernier scale is to the right of the zero mark on the main scale.
- Negative zero error: The zero mark on the Vernier scale is to the left of the zero mark on the main scale.
- Zero error calculation: error = C.V.S.D x L.C. where C.V.S.D is the coinciding vernier scale division.

Measuring Instruments: Screw Gage

MSR: Main scale reading
VSR: Vernier scale reading (usually represented as a fraction)
SD: Number of circular scale divisions
No zero error: When the zero of the main scale coincides with the "line" and the zero of the circular scale coincides with the reference line of main scale simultaneously.

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Description

This quiz covers the fundamental concepts of units and dimensions in physics. It explores the CGS and MKS systems, the relationship between physical quantities and their units, as well as the dimensional analysis of various physical quantities. Test your knowledge on this essential topic to solidify your understanding of measurement in physics.