Understanding Physical Quantities in Physics

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Questions and Answers

What are the dimensions of velocity in terms of mass, length, and time?

[M0L0T-1]

[M0L1T0]

[M0L1T-1] (correct)

[M1L0T-1]

How is acceleration formulated dimensionally?

[M0L2T-2]

[M1L0T-2]

[M0L1T-2] (correct)

[M1L1T-2]

What dimensional formula corresponds to pressure?

[M1L0T-2]

[M1L1T-2]

[M0L1T-2]

[M1L-1T-2] (correct)

Which of the following relates to the dimensions of work or energy?

[M1L2T-2] Signup and view all the answers

What is the dimensional formula for momentum?

[M1L1T-1] Signup and view all the answers

What are the dimensions of a in the equation related to volume V?

M1L5T-2 Signup and view all the answers

Which of the following statements about dimensionless quantities is true?

All trigonometric functions are dimensionless. Signup and view all the answers

What is the correct derivation of dimensions for pressure P in terms of M, L, and T?

M1L-1T-2 Signup and view all the answers

Which of the following quantities is dimensionless?

sin(θ) Signup and view all the answers

If V = L^3, what are the dimensions for V^2?

M0L6T0 Signup and view all the answers

What are the derived units of time t in terms of dimensions?

M0L0T1 Signup and view all the answers

In the expression F = sin(βt), what can we conclude about the dimensions of F?

F has dimensions of force. Signup and view all the answers

If the term loge(x) is used, what can be inferred about x?

x is a dimensionless quantity. Signup and view all the answers

What is the correct expression for mass in terms of velocity (V), force (F), and time (T)?

M = (Some Number) V^-1 F^1 T^1 Signup and view all the answers

Which of the following is the unit of force in the MKS system?

kg m/s^2 Signup and view all the answers

What dimension is used for energy according to the solution provided?

[M^0L^2T^-2] Signup and view all the answers

To express energy E in terms of V, F, and T, which equation correctly represents the relationship?

[E] = [V^1][F^1][T^1] Signup and view all the answers

If the mass is expressed in terms of fundamental quantities, what would be the value of c when deriving the energy relationship?

1 Signup and view all the answers

Which of the following statements about dimensional analysis is correct?

Dimensions can be expressed in combinations of basic quantities. Signup and view all the answers

When calculating the dimensions from $[E] = [M^a][L^b][T^c]$, what does 'a' represent when comparing energy and mass dimensions?

1 Signup and view all the answers

What is the dimension of force noted in the text?

[M^1L^1T^-2] Signup and view all the answers

Which expression correctly represents the relationship for T derived from dimensional analysis?

T = (Some Number) (m)^0 (λ)^(1/2) (g)^(-1/2) Signup and view all the answers

What is the value of 'c' when solving for the dimensions of T?

-1/2 Signup and view all the answers

What is the derived expression for the natural frequency (f) of a closed pipe based on dimensional analysis?

f = (Some Number) (λ)^(1/2) (ρ)^(1/2) (P)^0 Signup and view all the answers

How do you experimentally determine the quantity referred to as 'Some Number' in the context?

By measuring the length of the pendulum and its time period. Signup and view all the answers

From the dimensional analysis, what does the dimension M^(0)L^(0)T^(1) correspond to?

A time period Signup and view all the answers

Which of the following equations correctly balances the powers for mass (M) in the natural frequency equation?

0 = b + c Signup and view all the answers

What is the relationship between 'b' and 'c' derived from the dimensions of the natural frequency equation?

b + c = 0 Signup and view all the answers

When solving for the time period T, which of the following statements is true about the quantity represented by 'g'?

It is a constant that represents gravitational acceleration. Signup and view all the answers

What is the derived value for 'Some Number' when $ heta = 1m$ and T = 2 sec?

6.28 Signup and view all the answers

What is the dimensional formula for electric field E?

M1L1T–3A–1 Signup and view all the answers

Which of the following represents the correct dimensional formula for resistance R?

M1L2T–3A–2 Signup and view all the answers

What is the dimensional formula for permittivity in vacuum (ε0)?

M–1L–3T4A2 Signup and view all the answers

How is the capacitance C defined dimensionally?

M–1L–2T4A2 Signup and view all the answers

What is the dimensional formula for magnetic permeability in vacuum (μ0)?

M1L1T–2A–2 Signup and view all the answers

What does the Stefan's constant (σ) dimensionally represent?

M1L2T–2K–4 Signup and view all the answers

The inductance L has which of the following dimensional formulas?

M1L2T–2A–2 Signup and view all the answers

How is the thermal conductivity K dimensionally expressed?

M1L2T–2K–1 Signup and view all the answers

What is the dimensional formula for electrical potential V?

M1L2T–3A–1 Signup and view all the answers

What is the dimensional formula for magnetic field B?

M1L1T–2A–1 Signup and view all the answers

What is the equivalent of 6.67 × 10–11 kg s²/m³ in the CGS system?

6.67 × 10–8 gs²/cm³ Signup and view all the answers

To convert a speed of 90 km/hour to m/s, which factor is used?

Multiply by 18 Signup and view all the answers

Which of the following correctly converts a density of 2 g/cm³ into kg/m³?

2 × 10³ kg/m³ Signup and view all the answers

What is the value of 7 pm when converted into μm?

7 × 10⁻⁶ μm Signup and view all the answers

In dimensional analysis, which of the following units is called a dyne?

g·cm/s² Signup and view all the answers

What is the correct conversion factor to change 5 m/s to km/hour?

Multiply by 3.6 Signup and view all the answers

Which equation correctly expresses the conversion of acceleration from m/s² to cm/s²?

a = a × 10² Signup and view all the answers

What is the output velocity when converting 90 km/hour into m/s?

25 m/s Signup and view all the answers

Study Notes

Physical Quantities

Physical quantities are measurable quantities used to describe the laws of physics.
Examples include length, velocity, acceleration, force, time, pressure, mass, and density.
Physical quantities are categorized into three types: fundamental, derived, and supplementary.

Fundamental Quantities

These are basic quantities from which other quantities are derived.
Seven fundamental quantities are defined in the International System of Units (SI): length, mass, time, temperature, electric current, luminous intensity, and amount of substance.
These quantities are independent of each other.
Length (L), Mass (M), Time (T), Temperature (K), Electric Current (A), Luminous Intensity (Cd), Amount of Substance (mol).

Derived Quantities

Derived quantities are expressed in terms of fundamental quantities.
Examples include velocity, acceleration, force, momentum, work, energy, power, etc.
Derived quantities are related to fundamental quantities through equations.

Supplementary Quantities

Supplementary quantities are independent physical quantities needed to define other quantities such as plane angle and solid angle.

Dimensions of Physical Quantities

Dimensions represent the power to which fundamental quantities are raised to express a physical quantity.
The dimensions of a physical quantity are enclosed in square brackets [ ].
Example: [Length] = [L], [Mass] = [M], [Time] = [T]

Dimensional Formula

The representation of a physical quantity in terms of fundamental quantities with their respective powers is known as a dimensional formula.

Dimensional Analysis

Dimensional analysis is used to check the dimensional correctness of a physical equation.
The dimensions of the left-hand side (LHS) and the right-hand side (RHS) of an equation must be the same.

Dimensions of Physical Constants

Physical constants also have dimensions.
The dimensions of a physical constant can be determined from the equation in which it appears.

Some Special Features of Dimensions

Quantities can be added or subtracted only if they have the same dimensions.
Numbers are dimensionless.
Trigonometric, logarithmic, and exponential functions are dimensionless.

Uses of Dimensions

To check the correctness of a formula.
To derive new formulas.

SI Units

SI units are internationally accepted standard units for measuring physical quantities.
Examples include meters for length, kilograms for mass, seconds for time, etc...

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Description

This quiz covers the essential concepts of physical quantities in physics, including fundamental and derived quantities. You will explore how these quantities are measured and categorized, and their significance in the laws of physics. Test your knowledge on the International System of Units (SI) and their applications.