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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 \(a, b, c\).

Frequently Asked Questions

A physical quantity is a property of a system that can be measured and expressed numerically with a unit, such as length, mass, and time.?

A unit is a standard reference chosen to measure a physical quantity, e.g., metre for length, kilogram for mass.?

Physical quantities that are independent of other quantities, e.g., length, mass, time, electric current, temperature, amount of substance, luminous intensity.?

There are seven SI base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, luminous intensity.?

Metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).?

Quantities defined using base quantities (e.g., velocity, force); their units are combinations of base units (e.g., \(m\ s^{-1},\ kg\ m\ s^{-2}\).?

SI supplementary units are: radian (rad) for plane angle and steradian (sr) for solid angle.?

It is internationally accepted, coherent, and based on seven base units with well-defined standards, simplifying scientific communication.?

A system where derived units are obtained from base units without additional numerical factors, e.g., \(1\ N = 1\ kg\ m\ s^{-2}\).?

It is the expression of a physical quantity in terms of base dimensions, like \([M^aL^bT^c]\) for mass, length, and time powers.?

Velocity has dimensional formula \([LT^{-1}]\).?

Force has dimensional formula \([MLT^{-2}]\).?

In a physically meaningful equation, the dimensions of all terms on both sides must be the same.?

To check the dimensional consistency of equations, derive relations between quantities, and convert from one system of units to another.?

It cannot determine dimensionless constants (like 1/2, 2p), and it fails if quantities of different dimensions are added.?
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