Units & Measurement – True/False Deep Dive
NCERT Physics · Class 11 · Chapter 1

These True/False statements stress‑test your concepts of SI units, dimensions, dimensional analysis and dimensionless numbers — the hidden grammar behind every physics equation.

Start True/False Quiz ↓ View Dimension Capsules
L M T [P] = ML^-1T^-2 [E] = ML^2T^-2 Re, Mach → M^0L^0T^0 lₚ ∝ G^aħ^b c^c Track how units, dimensions and pure numbers weave through every True/False statement.
Focus Area
SI base & derived units
Concept Layer
Dimensions & analysis
Question Style
Concept traps & edge‑cases
Best For
Boards · JEE/NEET quick filters

Why These True/False Questions Matter

  • Entrance exams constantly use dimensional analysis to frame option‑elimination questions and to check whether you understand what is truly dimensionless.
  • Statements about SI base units, derived units like newton/joule and quantities such as Reynolds or Mach numbers are standard quick‑score areas.
  • Higher‑order questions on Planck length, gravitational constant and permittivity test whether you can combine dimensions of fundamental constants correctly.
  • Learning to reject false claims like “dimensionally correct ⇒ physically correct” prevents conceptual traps that appear in advanced JEE/NEET numericals.

Key Concepts Hidden in the Statements

SI Base vs Derived Units

Understand which quantities are base (L, M, T, I, K, mol, cd) and how units like newton and joule are constructed from them using simple algebraic relations.

Dimensions & Homogeneity

Use dimensional formulae such as [F] = MLT^{-2} or [P] = ML^{-1}T^{-2} and the principle of homogeneity to decide which equations can be physically acceptable.

Dimensionless Quantities

Recognise that ratios like Reynolds number, Mach number and many pure numbers have dimensions M^0L^0T^0, yet their numerical values need not be 1.

Power & Limits of Dimensional Analysis

Dimensional analysis helps in checking equations, deriving relations and converting units, but cannot give exact numerical constants or guarantee physical correctness.

Model Relations via DA

Relations like T ∝ √(l/g), vₑₛc ∝ √(GM/R) or satellite period vs orbital radius can be obtained up to dimensionless factors using dimensional reasoning alone.

Fundamental Constants & Planck Scale

Combining G, ħ and c to form Planck length illustrates how dimensions of constants lead to unique combinations like lₚ ∝ √(ħG/c³).

Important Dimension & Unit Capsules

Force (newton)
\[[F] = MLT^-2, 1 N = 1 kg m s^-2\]
Energy (joule)
\[[E] = ML^2T^-2, 1 J = 1 N\ m\]
Pressure
\[[P] = ML^-1T^-2, 1 Pa = 1\ N\ m^-2\]
Angular Momentum / h
\[[L] = [h] = ML^2T^-1\]
Gravitational Constant
\[[G] = M^-1L^3T^-2\]
Reynolds Number
\[Re = ρ v D / η → M^0L^0T^0\]
Planck Length
\[lₚ ∝ √(ħG / c³)\]
Use these as quick references when judging whether each statement is true, false or “missing a condition”.

What You Will Learn from These True/False Items

  • To separate correct and incorrect statements about SI base units, derived units and dimensionless quantities with confidence.
  • To recognise when two different physical quantities share the same dimensions (like torque and energy) even though their physical meaning differs.
  • To use dimensional homogeneity as a quick test for equations and to know where this method fails or needs additional physical input.
  • To reason about advanced constructs like Reynolds number, Mach number and Planck length using only dimensions and fundamental constants.
  • To avoid common myths such as “dimensionless ⇒ value 1” or “dimensionally correct ⇒ automatically physically correct”.

Exam Strategy & Preparation Tips for True/False

  • Underline phrases like “always”, “only”, “exact” and “uniquely” — then hunt for counter‑examples using simple cases and known formulas.
  • For any relation involving new constants, immediately write dimensions of each quantity and check if both sides match before thinking about physics details.
  • Remember that dimensional analysis cannot give you sin, cos or numerical factors; any statement claiming that analysis alone yields sin 2θ or exact coefficients is suspect.
  • Treat Reynolds and Mach numbers as pure ratios; if an option or statement gives them units, it is automatically false.
  • After each quiz run, rewrite the false statements into correct versions; this turns the T/F set into a compact conceptual summary for last‑minute revision.
Your Progress 0 / 25 attempted
Q 01 / 25
The International System of Units (SI) is built on seven base physical quantities and their corresponding base units.
Q 02 / 25
In SI, the metre is the base unit of length and the kilogram is the base unit of mass.
Q 03 / 25
In the SI system, the second is defined as the time taken by Earth to complete one rotation about its axis.
Q 04 / 25
Electric current is a base quantity in SI, while charge is a derived quantity.
Q 05 / 25
The plane angle measured in radians is treated as a dimensionless quantity in dimensional analysis.
Q 06 / 25
A derived quantity is any physical quantity that can be expressed algebraically in terms of base quantities.
Q 07 / 25
Velocity and speed always have different dimensions in mechanics.
Q 08 / 25
Pressure has the same dimensions as energy.
Q 09 / 25
A dimensionless physical quantity must always have the numerical value 1.
Q 10 / 25
The joule is an example of a derived SI unit formed from base units.
Q 11 / 25
The newton is the SI unit of force and can be written in base units as \(\text{kg m s}^{-2}\).
Q 12 / 25
The dimensional formula of energy and that of torque are different.
Q 13 / 25
A physically meaningful equation can relate quantities with different dimensions on the two sides.
Q 14 / 25
If two quantities have the same dimensions, they must represent the same physical concept.
Q 15 / 25
Dimensional analysis can be used to check whether a proposed physical formula is dimensionally consistent.
Q 16 / 25
Dimensional analysis can determine the exact numerical constant (like \(2\) or \(\pi\)) in a physical law.
Q 17 / 25
If an equation is dimensionally correct, it is guaranteed to be physically correct.
Q 18 / 25
The expression for kinetic energy \(E = \tfrac{1}{2} m v^2\) is dimensionally consistent with the dimensions of energy.
Q 19 / 25
The relation \(v = u + a t^2\) is dimensionally consistent for uniformly accelerated motion.
Q 20 / 25
If the period \(T\) of a simple pendulum depends only on its length \(l\) and gravitational acceleration \(g\), dimensional analysis predicts \(T \propto \sqrt{l/g}\).
Q 21 / 25
Dimensional analysis can suggest that the escape velocity from a planet is proportional to \(\sqrt{GM/R}\), where \(G\) is the gravitational constant, \(M\) the planet’s mass and \(R\) its radius.
Q 22 / 25
From dimensional analysis alone, one can derive the exact factor \(\sin 2\theta\) in the formula for the range of a projectile.
Q 23 / 25
For laminar flow in a horizontal pipe, dimensional analysis alone is sufficient to deduce that average speed must be proportional to the pressure gradient times the square of the radius divided by viscosity.
Q 24 / 25
The fact that the Reynolds number is dimensionless follows from expressing it as a combination of density, speed, length scale and viscosity in which all dimensional factors cancel.
Q 25 / 25
Because Planck length is built from \(G\), \(\hbar\) and \(c\), dimensional analysis can be used to express it uniquely as a product \(G^a \hbar^b c^c\) with specific exponents \(a, b, c\).
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