Classical Mechanics I: Master Newton's Laws and Mechanical Systems

Question 1

For a rigid body to be in equilibrium, which of the following conditions must be satisfied?

Accepted Answer

The net force acting on the body is zero.

Accepted Answer

The net torque acting on the body is zero.

Answer

The body is moving with constant velocity.

Answer

The body is at rest.

Question 2

A block of mass m is initially at rest on a frictionless horizontal surface. A constant horizontal force F is applied to the block. What will happen to the block?

Accepted Answer

The block will accelerate in the direction of the force.

Answer

The block will remain at rest.

Answer

The block will decelerate in the direction of the force.

Answer

The block will move in a circular path.

Question 3

A ball with a mass of 2 kg is initially moving east at 5 m/s. A force of 10 N is applied to the ball in the westward direction for 2 seconds. What is the ball's final velocity?

Accepted Answer

5 m/s west

Answer

1 m/s east

Answer

10 m/s east

Answer

10 m/s west

Question 4

In a mechanical system undergoing simple harmonic motion, what factor primarily determines the maximum distance from the equilibrium position?

Accepted Answer

Stiffness of the restoring force

Answer

Mass of the oscillating object

Answer

Damping coefficient

Question 5

In designing a vehicle's suspension system, which material property is most important to consider? Focus on properties that influence the system's ability to absorb and control road irregularities.

Accepted Answer

Stiffness

Answer

Density

Answer

Strength

Answer

Resistivity

Question 6

A body of mass 'm' is released from rest at a height 'h' above the ground. Neglecting air resistance, what is the speed 'v' of the body just before it hits the ground?

Accepted Answer

v = √(2gh)

Answer

v = √(gh)

Answer

v = gh

Answer

v = 2gh

Question 7

Define elasticity and explain how it influences a material's behavior under stress. Describe the various types of elastic moduli and provide examples of their applications.

Accepted Answer

Elasticity measures a material's ability to deform under stress and return to its original shape when the stress is removed. Elastic moduli relate stress and strain in a material.

Answer

Elasticity measures a material's strength, while elastic moduli measure its stiffness.

Answer

Elasticity measures a material's toughness, while elastic moduli measure its hardness.

Answer

Elasticity measures a material's density, while elastic moduli measure its weight.

Question 8

How does the eccentricity of a satellite's orbit influence the gravitational force acting upon it from the central body?

Accepted Answer

The eccentricity of the orbit alters the distance between the satellite and the central body, which in turn affects the gravitational force.

Answer

The eccentricity of the orbit has no impact on the gravitational force.

Answer

The gravitational force is consistently stronger when the eccentricity of the orbit is higher.

Question 9

A particle of mass m moves in a circular path of radius r with a constant speed v. The work done by the centripetal force acting on the particle over one complete revolution is:

Accepted Answer

Zero

Answer

1/2 mv^2

Answer

mv^2

Answer

2mv^2

Question 10

A block of mass m slides down an inclined plane of angle θ with a coefficient of kinetic friction μk. The acceleration of the block down the plane is:

Accepted Answer

g cos θ - μk g sin θ

Answer

g sin θ

Answer

g sin θ - μk g cos θ

Answer

g cos θ + μk g sin θ

Question 11

A ball is thrown vertically upward and reaches its maximum height in t seconds. The initial velocity of the ball is:

Accepted Answer

gt

Answer

gt/2

Answer

2gt

Answer

gt/4

Question 12

A car of mass m is traveling at a speed v and applies a braking force F. The stopping distance of the car is:

Accepted Answer

v^2 / (2F)

Answer

2v^2 / F

Answer

F v^2 / 2

Answer

F / (2v^2)

Question 13

A simple pendulum of length l and mass m swings with an amplitude θ. The potential energy of the pendulum at the highest point of its swing is:

Accepted Answer

mgl(1 - cos θ)

Answer

mgl cos θ

Answer

mgl(cos θ - 1)

Answer

mgl(sin θ - 1)

Question 14

A force of 20 N is applied to a block of mass 5 kg for 10 seconds. Calculate the impulse imparted to the block:

Accepted Answer

100 Ns

Answer

10 Ns

Answer

50 Ns

Answer

200 Ns

Question 15

The force required to accelerate an object of mass 'm' at a rate of 'a' is given by the equation:

Accepted Answer

F = ma

Answer

F = mv

Answer

F = mv^2

Answer

F = ma^2

Question 16

Momentum is a conserved quantity in an isolated system, meaning the total momentum remains constant over time.

Accepted Answer

True

Answer

False

Question 17

The work done by a force on an object is equal to the:

Accepted Answer

Change in kinetic energy of the object

Answer

Magnitude of the applied force

Answer

Displacement of the object

Answer

Negative of the potential energy of the object

Question 18

A simple pendulum demonstrates:

Accepted Answer

Simple harmonic motion

Answer

Forced oscillations

Answer

Damped oscillations

Answer

Anharmonic oscillations

Question 19

The formula for gravitational potential energy near the Earth's surface is:

Accepted Answer

U = mgh

Answer

U = mgv

Answer

U = mhv^2

Answer

U = mv^2g

Question 20

The coefficient of restitution primarily indicates the:

Accepted Answer

Elasticity of a collision

Answer

Inelasticity of a collision

Answer

Momentum transferred during a collision

Answer

Kinetic energy lost during a collision

Question 21

The rotational counterpart of linear momentum is:

Accepted Answer

Angular momentum

Answer

Torque

Answer

Moment of inertia

Answer

Rotational kinetic energy

Question 22

The trajectory of an object launched at an angle with a given velocity is most accurately described as:

Accepted Answer

A parabola

Answer

A straight line

Answer

A circle

Answer

An ellipse

Question 23

A 10 kg block is at rest on a rough horizontal surface. The coefficient of static friction between the block and the surface is 0.5. What is the minimum horizontal force needed to get the block moving?

Accepted Answer

50 N

Answer

20 N

Answer

100 N

Answer

25 N

Question 24

According to Newton's First Law of Motion, what happens to an object at rest or in motion if no external force acts on it?

Accepted Answer

It remains at rest or continues moving at constant velocity.

Answer

It accelerates.

Answer

It decelerates.

Question 25

Which of the following is the unit of work and energy?

Accepted Answer

Joule

Answer

Newton

Answer

Watt

Question 26

Which force can be stored as potential energy?

Accepted Answer

Gravity

Answer

Friction

Answer

Air resistance

Question 27

At the highest point of a projectile's trajectory, which energy is at its maximum?

Accepted Answer

Potential energy

Answer

Kinetic energy

Answer

Both kinetic and potential energies

Question 28

What condition must be met for an object to be in static equilibrium?

Accepted Answer

Zero net force and zero net torque

Answer

Zero net force and non-zero net torque

Answer

Non-zero net force and zero net torque

Question 29

Momentum is defined as the product of an object's mass and velocity. True or False?

Accepted Answer

True

Answer

False

Question 30

Energy is a conserved quantity, meaning it can be neither created nor destroyed. True or False?

Accepted Answer

True

Answer

False

Question 31

The work done by a force over a displacement is calculated using the dot product of the force vector and the displacement vector. True or False?

Accepted Answer

True

Answer

False

Question 32

Kinetic energy of an object is calculated as half of its mass multiplied by the square of its velocity. True or False?

Accepted Answer

True

Answer

False

Question 33

A projectile launched with an initial velocity will exhibit a parabolic trajectory. True or False?

Accepted Answer

True

Answer

False

Question 34

The center of mass of a particle system is the point where the net torque acting on the system is zero. True or False?

Accepted Answer

True

Answer

False

Question 35

A 5kg block slides across a frictionless surface with a velocity of 10 m/s. Determine the work done by friction over a distance of 20m.

Accepted Answer

0 J

Answer

50 J

Answer

100 J

Answer

200 J

Question 36

In which industry are the principles of classical mechanics least likely to be applied?

Accepted Answer

Fashion Design

Answer

Mechanical Engineering

Answer

Civil Engineering

Answer

Aerospace Engineering

Question 37

What action will result in an increase in the natural frequency of a vibrating system with a fixed mass?

Accepted Answer

Increase the stiffness

Answer

Decrease the stiffness

Answer

Add a damping force

Answer

Increase the mass

Question 38

A rigid body rotates around a fixed axis with an angular velocity of 2 rad/s. If the net torque acting on the body is tripled, what will happen to its angular acceleration?

Accepted Answer

It will triple.

Answer

It will halve.

Answer

It will stay the same.

Answer

It cannot be determined without knowing the moment of inertia.

Question 39

In physics, power is defined as the rate of:

Accepted Answer

Work done per unit time

Answer

Force

Answer

Displacement

Answer

Time

Question 40

A car is traveling at a constant speed of 20 m/s. What is its acceleration?

Accepted Answer

0 m/s²

Answer

20 m/s²

Answer

-9.8 m/s²

Answer

9.8 m/s²

Question 41

A ball is thrown vertically upward with an initial velocity of 10 m/s. What is its maximum height above the point of projection?

Accepted Answer

~5.1 m

Answer

~10.2 m

Answer

~2.5 m

Question 42

A block is sliding down an inclined plane with an angle of 30°. What is the acceleration of the block parallel to the plane?

Accepted Answer

g * sin(30°)

Answer

-g * cos(30°)

Answer

g * cos(30°)

Answer

-g * sin(30°)

Question 43

A ball is dropped from a height of 10 m. What is its kinetic energy just before it hits the ground?

Accepted Answer

100 J

Answer

0 J

Answer

50 J

Answer

200 J

Question 44

A rigid body is rotating about a fixed axis with an angular velocity ω. The moment of inertia of the body is I. What is the kinetic energy of the body?

Accepted Answer

K = 1/2⋅I⋅ω²

Answer

K = I/ω

Answer

K = ω/I

Answer

K = I⋅ω

Question 45

A system consists of two particles of masses m1 and m2, which are moving in the same direction with velocities v1 and v2, respectively. What is the total momentum of the system?

Accepted Answer

P = m1⋅v1 + m2⋅v2

Answer

P = (m1⋅v1) / (m2⋅v2)

Answer

P = (m2⋅v2) / (m1⋅v1)

Answer

P = m1⋅v1 - m2⋅v2

Question 46

A spring of spring constant k is stretched a distance x from its equilibrium position. What is the elastic potential energy stored in the spring?

Accepted Answer

U = 1/2⋅k⋅x²

Answer

U = k⋅x

Answer

U = x²/2⋅k

Answer

U = k/x²

Question 47

Which of the following statements accurately represents Newton's second law of motion?

Accepted Answer

F = ma

Answer

F = mv/t

Answer

F = ½mv²

Answer

F = mv

Question 48

Identify the force that is considered conservative.

Accepted Answer

Gravitational force

Answer

Frictional force

Answer

Tension force

Answer

Air resistance force

Question 49

Which of the following physical quantities is a scalar?

Accepted Answer

Mass

Answer

Velocity

Answer

Force

Answer

Acceleration

Question 50

A ball is rolling on a flat surface with a constant velocity. In this scenario, what is the net force acting upon the ball?

Accepted Answer

Zero

Answer

Gravitational force

Answer

Frictional force

Question 51

Identify the SI unit of energy.

Accepted Answer

Joule

Answer

Second

Answer

Meter

Answer

Newton

Question 52

Which of the following is NOT a valid unit of work?

Accepted Answer

N/m

Answer

J

Answer

Nm

Answer

ft-lb

Question 53

Which of the following expressions correctly represents kinetic energy?

Accepted Answer

1/2 mv^2

Answer

mv^3

Answer

1/2 m^2 v

Answer

mv

Question 54

A spring with a spring constant of 100 N/m is stretched by 0.2 m. How much potential energy is stored in the spring?

Accepted Answer

2 J

Answer

1 J

Answer

4 J

Answer

8 J

Question 55

Which of the following is the correct equation for torque?

Accepted Answer

F x r

Answer

F + r

Answer

F / r

Answer

r / F

Question 56

According to Newton's second law, force is equal to the:

Accepted Answer

Mass of an object multiplied by its acceleration

Answer

Mass of an object divided by its acceleration

Answer

Acceleration of an object divided by its mass

Answer

Acceleration of an object multiplied by its velocity

Question 57

The work done by a force is positive when:

Accepted Answer

The force and displacement are in the same direction

Answer

The force is zero

Answer

The force and displacement are in opposite directions

Question 58

Which of the following is NOT a type of mechanical energy?

Accepted Answer

Radiant energy

Answer

Potential energy

Answer

Elastic energy

Answer

Kinetic energy

Question 59

A rigid body rotates about a fixed axis with angular velocity ω and angular acceleration α. Its tangential acceleration is given by:

Accepted Answer

αr

Answer

α/r

Answer

ω^2r

Answer

ωr

Question 60

The kinetic energy of a particle of mass 'm' moving with a velocity 'v' is expressed by which formula?

Accepted Answer

1/2 * m * v^2

Answer

2 * m * v^2

Answer

1/4 * m * v^2

Answer

m * v

Question 61

Which of the following physical quantities is a vector quantity?

Accepted Answer

Velocity

Answer

Mass

Answer

Time

Answer

Temperature

Question 62

A system is considered to be in equilibrium when:

Accepted Answer

Both the net force and the net torque acting on it are zero.

Answer

The net torque acting on it is zero.

Answer

The net force acting on it is zero.

Question 63

A key characteristic of a simple harmonic oscillator is that:

Accepted Answer

It experiences a restoring force proportional to its displacement.

Answer

It moves with constant velocity.

Answer

It oscillates with constant displacement.

Answer

It experiences constant acceleration.

Question 64

As a block of mass 'm' slides down an inclined plane with angle of inclination 'theta', what is its acceleration?

Accepted Answer

g * sin(theta)

Answer

g * tan(theta)

Answer

g

Answer

g * cos(theta)