Classical Mechanics Quizzes: Test Your Understanding

Question 1

In special relativity, time dilation is a consequence of:

Accepted Answer

The constant speed of light

Answer

The equivalence of mass and energy

Answer

The curvature of spacetime

Answer

The expansion of the universe

Question 2

The motion of a particle in central potential is:

Accepted Answer

Planetary

Answer

Harmonic

Answer

Projectile

Answer

Brownian

Question 3

The equation of motion for a particle in a conservative force field is:

Accepted Answer

F = -∇V

Answer

F = ma

Answer

a = v^2/r

Answer

v = ωr

Question 4

Hamilton's equations describe the time evolution of a system's:

Accepted Answer

Generalized coordinates (q) and generalized momenta (p):  (dq/dt = ∂H/∂p) and (dp/dt = -∂H/∂q)

Answer

Generalized coordinates (q) and generalized velocities (q̇): (dq/dt = q̇) and (dp/dt = 0)

Answer

Generalized velocities (q̇) and generalized accelerations (q̈): (dq/dt = q̈) and (dp/dt = q̈)

Answer

Coordinates (x, y, z) and momenta (px, py, pz):  [(dx/dt) = (px/m), (dy/dt) = (py/m), (dz/dt) = (pz/m)] and [(dp/dt)x = 0, (dp/dt)y = 0, (dp/dt)z = 0]

Question 5

Which of the following is NOT a conserved quantity in classical mechanics?

Accepted Answer

Entropy

Answer

Linear momentum

Answer

Angular momentum

Answer

Total energy

Question 6

The resonance frequency (f) of a system is the frequency at which:

Accepted Answer

The system oscillates with maximum amplitude

Answer

The system possesses maximum energy

Answer

The system's period of oscillation is minimum

Answer

The system experiences maximum damping

Question 7

The Lagrangian formulation of classical mechanics places emphasis on the principle of:

Accepted Answer

Least action

Answer

Conservation of energy

Answer

Conservation of momentum

Answer

Hamilton's principle

Question 8

In an isolated system, the total momentum:

Accepted Answer

Is conserved.

Answer

Increases.

Answer

Decreases.

Answer

Cannot be determined.

Question 9

Angular momentum of a system remains constant if:

Accepted Answer

No external torque acts on the system.

Answer

The system is in rotational equilibrium.

Answer

The total energy of the system is constant.

Answer

The system is in linear motion.

Question 10

Which of the following is the SI unit of torque?

Accepted Answer

Newton-meter

Answer

Joule-second

Answer

Watt

Answer

Pascal

Question 11

Which of the following is **not** a Newton's law of motion?

Accepted Answer

The momentum of a closed system remains constant.

Answer

An object at rest remains at rest unless acted upon by an unbalanced force.

Answer

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Answer

For every action, there is an equal and opposite reaction.

Question 12

The Hamiltonian for a particle of mass m moving in a potential V(x) is:

Accepted Answer

H = (1/2m)p^2 + V(x)

Answer

H = (1/2m)p^2 - V(x)

Answer

H = V(x) + (1/2m)p^2

Answer

H = V(x) - (1/2m)p^2

Question 13

The relativistic kinetic energy of a particle is:

Accepted Answer

K = mc^2γ - mc^2

Answer

K = (1/2)mv^2

Answer

K = mc^2γ^2 - mc^2

Answer

K = mc^2 - (1/2)mv^2

Question 14

The mass-energy equivalence formula is:

Accepted Answer

E = mc^2

Answer

E = mv^2

Answer

m = E/c^2

Answer

v = E/m

Question 15

According to Newton's second law of motion, the force acting on an object is:

Accepted Answer

Equal to the product of its mass and acceleration

Answer

Proportional to its acceleration

Answer

Inversely proportional to its acceleration

Answer

Independent of its acceleration

Question 16

Which expression represents the Lagrangian of a particle in motion under a central potential?

Accepted Answer

Kinetic energy minus potential energy

Answer

Kinetic energy plus potential energy

Answer

Kinetic energy multiplied by potential energy

Answer

Potential energy divided by kinetic energy

Question 17

For a particle moving in a circular path, the centripetal force acting on it is:

Accepted Answer

Directed toward the centre of the circle

Answer

Directed away from the centre of the circle

Answer

Zero

Answer

Non-zero and perpendicular to the velocity

Question 18

The differential equation that describes a damped harmonic oscillator is:

Accepted Answer

mx'' + bx' + kx = 0

Answer

mx'' + cx' = 0

Answer

mx'' = 0

Answer

bx' + kx = 0

Question 19

The Lagrangian of a system is a function of which variables?

Accepted Answer

Position and velocity

Answer

Position and time

Answer

Velocity and time

Answer

Mass and acceleration

Question 20

A particle is moving in a circular path of radius R. Which of the following expressions represents the centripetal force acting on the particle?

Accepted Answer

F = mv²/R

Answer

F = 2mv/R

Answer

F = mR²/v

Answer

F = 2πmv/R

Question 21

Which of the following is a vector quantity?

Accepted Answer

Velocity

Answer

Mass

Answer

Time

Answer

Energy

Question 22

A system is said to be in equilibrium when the net force acting on it is:

Accepted Answer

Zero

Answer

Constant

Answer

Increasing

Answer

Decreasing

Question 23

The Hamiltonian of a system is a function of which variables?

Accepted Answer

Position and momentum

Answer

Velocity and time

Answer

Energy and time

Answer

Mass and acceleration

Question 24

According to the equivalence principle in general relativity, which of the following is true?

Accepted Answer

Gravitational mass and inertial mass are identical for all objects.

Answer

Gravitational mass and inertial mass are distinct for all objects.

Answer

The speed of light varies in different inertial frames of reference.

Answer

The curvature of spacetime is a result of dark matter.

Question 25

According to Newton's second law, the force acting on an object is directly proportional to its:

Accepted Answer

Acceleration

Answer

Mass

Answer

Momentum

Answer

Kinetic energy

Question 26

In the context of special relativity, which statement regarding the speed of light is correct?

Accepted Answer

It remains constant for all observers

Answer

It varies depending on the observer's frame of reference

Answer

It is proportional to the object's mass

Answer

It is infinite

Question 27

What physical quantity does the Hamiltonian function represent in a system?

Accepted Answer

Energy

Answer

Momentum

Answer

Phase space

Answer

Lagrangian

Question 28

Which condition is necessary for a rigid body to be in equilibrium?

Accepted Answer

Both the net force and net torque acting on the body must be zero

Answer

Only the net force acting on the body must be zero

Answer

Only the net torque acting on the body must be zero

Answer

The body must be at rest

Question 29

Which of the following is NOT a conserved quantity in classical mechanics?

Accepted Answer

Electric charge

Answer

Energy

Answer

Momentum

Answer

Angular momentum

Question 30

Lagrangian formulation in classical mechanics primarily emphasizes:

Accepted Answer

Generalized coordinates and generalized forces

Answer

Energy and momentum

Answer

Position and velocity

Answer

Force and acceleration

Question 31

Motions that occur in the absence of external forces acting on a system are referred to as:

Accepted Answer

Free motions

Answer

Driven motions

Answer

Damped motions

Answer

Forced motions

Question 32

The angular momentum of a rotating object is a measure of its:

Accepted Answer

Rotational inertia

Answer

Linear momentum

Answer

Kinetic energy

Answer

Potential energy

Question 33

Which of the following is NOT an example of a non-inertial reference frame?

Accepted Answer

A stationary building

Answer

An accelerating car

Answer

A rotating turntable

Answer

A moving train

Question 34

The concept of generalized coordinates allows us to describe the motion of a system with:

Accepted Answer

Multiple degrees of freedom

Answer

One degree of freedom

Answer

Two degrees of freedom

Answer

Only translational degrees of freedom

Question 35

According to Newton's second law, the force (F) acting on an object with mass (m) is directly proportional to its acceleration (a). Mathematically, it is expressed as:

Accepted Answer

F = ma

Answer

F = mv

Answer

F = ma^2

Answer

F = mv^2

Question 36

In Lagrangian mechanics, the Lagrangian (L) is a function that describes the system's total energy. It is defined as the difference between the kinetic energy (T) and potential energy (V):

Accepted Answer

L = T - V

Answer

L = T + V

Answer

L = V - T

Answer

L = 2T - V

Question 37

In Hamiltonian mechanics, the Hamiltonian (H) is a function that describes the total energy of the system. It is expressed as the sum of kinetic energy (T) and potential energy (V):

Accepted Answer

H = T + V

Answer

H = T - V

Answer

H = V - T

Answer

H = 2T + V

Question 38

The Lorentz transformation relates measurements made in two inertial frames moving at different speeds in different directions according to Einstein's theory of:

Accepted Answer

Special relativity

Answer

Classical mechanics

Answer

General relativity

Answer

Quantum mechanics

Question 39

According to Newton's second law of motion, the relationship between an object's mass (m), velocity (v), and force (F) is best described by which equation?

Accepted Answer

F = ma

Answer

E = mc^2

Answer

v = u + at

Answer

s = ut + 1/2 at^2

Question 40

In classical mechanics, the Lagrangian formulation involves minimizing a quantity known as the:

Accepted Answer

Action

Answer

Potential energy

Answer

Kinetic energy

Answer

Momentum

Question 41

In the Hamiltonian formulation of classical mechanics, finding the stationary point of which function is crucial?

Accepted Answer

Hamiltonian

Answer

Lagrangian

Answer

Energy

Answer

Momentum

Question 42

The equation of motion for a simple harmonic oscillator is:

Accepted Answer

m(d^2x/dt^2) + kx = 0

Answer

m(d^2x/dt^2) - kx = 0

Answer

m(d^3x/dt^3) + kx = 0

Answer

m(d^3x/dt^3) - kx = 0

Question 43

In classical mechanics, which of the following is a scalar quantity?

Accepted Answer

Mass

Answer

Velocity

Answer

Momentum

Question 44

According to Newton's second law of motion, which of the following accurately describes the relationship between an object's acceleration, the net force acting on it, and its mass?

Accepted Answer

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Answer

The momentum of an object is equal to the product of its mass and velocity.

Answer

The force acting on an object is equal to its acceleration multiplied by its mass.

Question 45

For a simple harmonic oscillator with mass 'm' and angular frequency 'ω', which of the following expressions represents its Hamiltonian?

Accepted Answer

H = (p²/2m) + (1/2)mw²x²

Answer

H = (p²/2m)x²

Answer

H = (p²m) + (1/2)w²x

Answer

H = (1/2)mw²x²

Question 46

In a two-dimensional projectile motion scenario, which of the following equations accurately describes the trajectory of the projectile?

Accepted Answer

x = ut cosθ, y = ut sinθ - (1/2)gt²

Answer

x = ut, y = (1/2)gt²

Answer

x = ut sinθ, y = ut cosθ - (1/2)gt²

Question 47

In the context of Hamiltonian systems, which of the following characteristics accurately defines a Hamiltonian system?

Accepted Answer

A system with a constant energy.

Answer

A system with a constant angular momentum.

Answer

A system with a constant Lagrangian.

Answer

A system with a constant momentum.