Physics Unit and Measurements Quiz

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Questions and Answers

What is the dimension of angular velocity?

$T^{-1}$

$L^1 T^{-1}$ (correct)

Zero

$L^1$

What is the SI unit of power?

Watt (correct)

Electricity

Energy

Force

Which of the following expresses temperature as a derived quantity?

Length, mass and time

Length and mass

Mass and time

None (correct)

The dimensional formula of stress is equivalent to which of the following?

Pressure Signup and view all the answers

What is the dimension of strain?

$M^1 L^0 T^0$ Signup and view all the answers

If 1 Joule of work is done in 1 second, what is the resulting measurement in Watts?

1 Watt Signup and view all the answers

Which physical dimensions cannot be derived from temperature?

Energy Signup and view all the answers

Which dimensional formula correctly represents the unit of pressure?

$M L^{-1} T^{-2}$ Signup and view all the answers

What characterizes a non-conservative force?

The work done depends on the path taken. Signup and view all the answers

How is linear momentum (p) defined?

It is the product of mass and velocity. Signup and view all the answers

What is the SI unit of impulse?

Ns Signup and view all the answers

When a bullet is fired from a gun, what happens to the gun's motion?

It recoils backward in the opposite direction of the bullet. Signup and view all the answers

What is the relationship described by impulse and momentum?

Impulse is the change in momentum. Signup and view all the answers

What is the mathematical expression for recoil velocity of a gun when a bullet is fired?

$V = -\frac{m v}{M}$ Signup and view all the answers

What dimensions represent linear momentum?

$MLT^{-1}$ Signup and view all the answers

Which of the following examples represents a non-conservative force?

Air drag Signup and view all the answers

What is the dimensional formula for acceleration?

$M L T^{-2}$ Signup and view all the answers

Which of the following is the dimension of thermal conductivity?

$M L T^{-3} K^{-1}$ Signup and view all the answers

What do the dimensions of a physical quantity represent?

The powers of fundamental units needed to represent it Signup and view all the answers

Which of the following represents the dimension for the quantity of velocity?

$L T^{-1}$ Signup and view all the answers

Which statement correctly defines impulsive force?

A large force acting on a body for a short time. Signup and view all the answers

How is the dimension of density expressed?

$M L^{-3}$ Signup and view all the answers

What does Newton's 1st Law of Motion state?

An object will remain at rest or in uniform motion unless acted upon by an external force. Signup and view all the answers

From the expression for thermal conductivity, which quantity appears in its dimensional analysis that is crucial for the representation?

Temperature (K) Signup and view all the answers

According to Newton's 2nd Law, how is force measured?

Force equals mass times acceleration: $F = ma$. Signup and view all the answers

Which of the following correctly describes impulse?

Impulse is the change in linear momentum. Signup and view all the answers

In the equation for acceleration, which physical quantity provides the base for dimensional analysis?

Time (t) Signup and view all the answers

What is the correct representation of the dimension of the quantity represented by the equation $k = \frac{ΔQ}{Δt Δθ}$?

$M L T^{-3} K^{-1}$ Signup and view all the answers

Which principle relates force to momentum change in an object?

The rate of change of momentum is proportional to the impressed force. Signup and view all the answers

What is the SI unit of force?

Newton Signup and view all the answers

What does Newton's 3rd Law of Motion state?

To every action, there is an equal and opposite reaction. Signup and view all the answers

Which of the following is an example of an impulsive force?

Kicking a football. Signup and view all the answers

What is the unit of the constant 𝑐 in the equation based on the principle of dimensional homogeneity?

m/s² Signup and view all the answers

Which term represents the maximum fractional error in density 𝜌 as derived from the dimensions?

$rac{∆ ho}{ ho}$ Signup and view all the answers

How is the formula $S = ut + rac{1}{2}at^2$ verified for dimensional correctness?

By confirming all terms have a dimension of $L$ Signup and view all the answers

What is the factor affecting centripetal force 𝑭 according to the principle discussed?

Mass, velocity, and radius Signup and view all the answers

What does the expression $log ho = log M - log rac{eta}{r^2} - log l$ simplify to?

log 𝜌 = log 𝑀 - 2 log 𝑟 - log 𝑙 Signup and view all the answers

When calculating dimensions, which term confirms the dimensional consistency in the equation?

Dimensions of all terms in the formula Signup and view all the answers

What does the equation $rac{∆ ho}{ ho} = rac{∆M}{M} + 2rac{∆r}{r} + rac{∆l}{l}$ represent?

Total relative error in density Signup and view all the answers

What conclusion can be drawn from the dimension analysis of the equation regarding dimensions of velocity?

Velocity must have dimensions of $LT^{-1}$ Signup and view all the answers

Study Notes

Unit and Measurements

The SI unit of power is the Watt.
1 Watt is equal to 1 Joule of work done in 1 second.
Temperature is a fundamental physical quantity and cannot be expressed as a derived quantity in terms of other physical quantities.
The dimensional formula of stress is the same as pressure; both are represented as 𝑀𝐿−1 𝑇 −2.
The dimension of strain is 𝑴𝟎 𝑳𝟎 𝑻𝟎.
The dimension of thermal conductivity is 𝑴𝑳𝑻−𝟑 𝑲−1.
the dimension of physical quantity: The dimension of a physical quantity are the powers to which the fundamental unit of mass (M), length (L), time (T), temperature (K), electric current (A) have to be raised in order to completely represent that physical quantity.
Example: Dimension of velocity = 𝐿𝑇 −1 and Dimension of density = 𝑀𝐿−3
To check if an equation is dimensionally correct, make sure every term in the equation has the same units.
Calculating Maximum Percentage Error for Density:
- Density is given by: 𝜌 = 𝑀 / 𝜋𝑟 2 𝑙
- Take the logarithm of both sides: log 𝜌 = log 𝑀 − log 𝜋 − 2 log 𝑟 − log 𝑙
- Differentiate both sides: ∆𝜌 / 𝜌 = ∆𝑀 / 𝑀 + 2 ∆𝑟 / 𝑟 + ∆𝑙 / 𝑙
- For Maximum fractional error of 𝜌, make all signs positive.
The formula for maximum percentage errors in density is: ∆𝜌 ∆𝑀 ∆𝑟 ∆𝑙 𝜌 = 𝑀 +2 𝑟 + 𝑙

Force and Motion

Linear Momentum is defined as the product of the mass of the body and its velocity.
Linear Momentum is measured in kilogram meters per second (kg⋅m/s), and the dimensional formula is 𝑀𝐿𝑇 −1
Impulse is the product of force and interval of time for which the force acts on a body. Impulse is measured in Newton Seconds (Ns), and the dimensional formula is 𝑀𝐿𝑇 −1
Impulse is equivalent to the change in linear momentum.
Impulsive force is a large amount of force acting on a body for a very small interval of time. Impulsive forces are measured in Newtons (N), and the dimensional formula is 𝑀𝐿𝑇 −2
The principle of conservation of linear momentum states that in a closed system, the total linear momentum is conserved.
Recoil velocity of a gun can be calculated using the principle of conservation of linear momentum:
- Let 𝑀 = mass of the gun, 𝑉 = velocity of the gun, 𝑚 = mass of the bullet, 𝑣 = velocity of the bullet
- Before firing, the total momentum, 𝑀𝑉 + 𝑚𝑣 = 0
- Therefore, the recoil velocity is: 𝑽 = − 𝒎𝒗 / 𝑀 (the negative sign shows that the direction of the recoil velocity is opposite to the direction of the bullet).
Newton’s Laws of Motion:
- First Law: Every body continues in its state of rest or of uniform motion in a straight line, unless it is compelled by some external force to change that state.
- Second Law: The rate of change of momentum of a body is directly proportional to the force applied on it and the change occurs in the direction of the applied force.
- Third Law: To every action, there is an equal and opposite reaction.
Non-conservative force:
- Work done by a non-conservative force depends on the path taken.
- A non-conservative force causes a change in mechanical energy.
- Examples: Air drag and friction.

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Description

Test your knowledge on units and measurements in physics with this quiz. Questions cover topics such as SI units, dimensional formulas, and physical quantities. Great for students learning the fundamentals of physics.