Dynamics in Mechanical Systems: Motion, Forces, and Energy

Question 1

In the study of rigid body dynamics, which force is NOT considered fundamental?

Accepted Answer

Electromagnetic force

Answer

Contact force

Answer

Gravitational force

Answer

Normal force

Question 2

According to Newton's second law of motion, which factor directly and proportionally affects an object's acceleration?

Accepted Answer

Net force acting on the object

Answer

Mass of the object

Answer

Velocity of the object

Answer

Displacement of the object

Question 3

A particle of mass (m) moves in a circular path of radius (r) with a constant speed (v). What is the force acting on the particle?

Accepted Answer

F = mv^2/r

Answer

F = mv^2r

Answer

F = mr^2/v

Answer

F = mv/r

Question 4

A particle of mass m is moving in a circular path of radius r with a constant speed v. The force acting on the particle is:

Accepted Answer

F = mv^2/r

Answer

F = mv^2r

Answer

F = mr^2/v

Answer

F = v^2/mr

Question 5

A particle of mass m moves in a straight line with velocity v. The force acting on the particle is F = -kv^3, where k is a positive constant. What happens to the particle's motion?

Accepted Answer

The particle slows down and eventually stops.

Answer

The particle moves with constant acceleration.

Answer

The particle moves with constant velocity.

Answer

The particle speeds up in the direction of its motion.

Question 6

A particle moves in a straight line with constantly increasing velocity. Which statement about its acceleration is correct?

Accepted Answer

Acceleration is always in the same direction as velocity.

Answer

Acceleration is always in the opposite direction as velocity.

Answer

Acceleration is always perpendicular to velocity.

Answer

Acceleration is always zero.

Question 7

Identify why a system consisting of a ball thrown vertically upward is deemed conservative:

Accepted Answer

Constant mechanical energy within the system

Answer

Negligible net force acting upon the system

Answer

Unvarying potential energy of the system

Answer

Invariable kinetic energy of the system

Question 8

A rigid body is rotating about a fixed axis through its center of mass. Which of the following quantities remains constant during rotation?

Accepted Answer

Angular momentum

Answer

Linear momentum

Answer

Kinetic energy

Answer

Potential energy

Question 9

According to the fundamental theorem of angular momentum, when is angular momentum conserved?

Accepted Answer

When there is no external torque acting on the system.

Answer

When the moment of inertia is constant.

Answer

When the object is rotating at a constant speed.

Answer

When the object is at rest.

Question 10

Newton's second law of motion states that the force acting on an object is directly proportional to its mass and acceleration. Which of the following equations correctly represents this relationship?

Accepted Answer

F = ma

Answer

F = m/a

Answer

a = Fm

Answer

a = m/F

Question 11

A rigid sphere with mass 'm' and radius 'R' rotates around a fixed axis through its center. Determine the kinetic energy of the rotating sphere.

Accepted Answer

KE = (1/2)Iω^2

Answer

KE = (1/2)mω^2

Answer

KE = (1/2)Iω

Answer

KE = Iω^3

Question 12

According to Newton's second law of motion, which factor does NOT directly affect an object's acceleration?

Accepted Answer

Velocity

Answer

Force

Answer

Mass

Question 13

A particle moves along a straight path with a constant acceleration. Which graph best shows the particle's velocity over time?

Accepted Answer

A straight line with a positive slope

Answer

A straight line with a negative slope

Answer

A parabola opening upwards

Answer

A parabola opening downwards

Question 14

A rigid body rotates about a fixed axis with an angular velocity of ω. What is the angular momentum of the body about an axis parallel to the axis of rotation and passing through the center of mass?

Accepted Answer

Iω

Answer

2Iω

Answer

Iω/2

Answer

0

Question 15

According to Newton's third law of motion, if object A exerts a force of 10 N on object B, what force does object B simultaneously exert on object A?

Accepted Answer

10 N in the opposite direction

Answer

20 N in the same direction

Answer

5 N in the opposite direction

Answer

15 N in the same direction

Question 16

An external force acting on an object can alter its state of motion. What is the primary effect of this force on the object?

Accepted Answer

Changes the object's velocity or acceleration

Answer

Alters the object's mass

Answer

Modifies the object's volume

Answer

Counteracts the object's weight

Question 17

A particle moves along a straight path with a constant, non-zero acceleration. Which of the following statements best describes the particle's motion?

Accepted Answer

The particle's acceleration remains constant.

Answer

The particle's velocity remains constant.

Answer

The particle's displacement remains constant.

Answer

Both the particle's velocity and displacement remain constant.

Question 18

A car with a mass of 1000 kilograms moves at a constant speed of 20 meters per second. What is the total force acting on the car?

Accepted Answer

0 Newtons

Answer

1000 Newtons

Answer

20000 Newtons

Answer

10000 Newtons

Question 19

Rotating machines can vibrate due to uneven mass distribution. What is dynamic balancing, and describe two methods used to balance such machines?

Accepted Answer

Dynamic balancing involves adjusting the mass distribution to minimize vibrations. One method is adding or removing weights at specific locations.

Answer

Dynamic balancing involves spinning the machine faster than its natural frequency to reduce vibrations.

Answer

Dynamic balancing is only used in machines with high-speed rotating parts.

Question 20

In a fluid flowing through a pipe with varying cross-sectional area, how do velocity and pressure change as the area decreases?

Accepted Answer

Velocity increases, pressure decreases

Answer

Velocity decreases, pressure increases

Answer

Both velocity and pressure increase

Answer

Both velocity and pressure decrease

Question 21

A body of mass 10 kg is under the action of a force F = (5t^2 + 10) N, where t is in seconds. Calculate the work done by this force on the body in the first 5 seconds.

Accepted Answer

1575 J

Answer

1375 J

Answer

1775 J

Answer

1975 J

Question 22

Which of the following is a scalar quantity?

Accepted Answer

Energy

Answer

Velocity

Answer

Acceleration

Answer

Force

Question 23

Which of the following is a conservative force?

Accepted Answer

Gravity

Answer

Friction

Answer

Tension

Answer

Air resistance

Question 24

A spring with a spring constant k is stretched by an amount Δx from its equilibrium position. What is the elastic potential energy stored in the spring?

Accepted Answer

1/2 kΔx^2

Answer

kΔx^2

Answer

1/2 Δx^2 / k

Answer

Δx^2 / k

Question 25

A particle's displacement is given by the function s(t) = t³ - 6t² + 9t. What is the particle's acceleration at t = 3 seconds?

Accepted Answer

6 m/s²

Answer

0 m/s²

Answer

-6 m/s²

Question 26

A particle with mass 'm' moves at a constant velocity. A force 'F' is applied in the direction of its motion. What is the power delivered by the force?

Accepted Answer

Fv, as power is the product of force and velocity.

Answer

Zero, since the force is constant.

Answer

F/v, as power is the ratio of force to velocity.

Answer

Fm, as power is the product of force and mass.

Question 27

In a simple harmonic oscillator, how does the amplitude of the oscillation affect the system's total energy? Explain the mathematical relationship between amplitude and energy.

Accepted Answer

The total energy is proportional to the square of the amplitude.

Answer

The total energy is inversely proportional to the amplitude.

Answer

The total energy is independent of the amplitude.

Answer

The total energy is directly proportional to the amplitude.

Question 28

In mechanical systems, damping refers to the process that causes oscillations to gradually decrease in amplitude. Explain how damping affects the behavior of a system.

Accepted Answer

Damping reduces oscillation amplitude by dissipating energy through friction or other resistive forces.

Answer

Damping increases oscillation amplitude.

Answer

Damping is only significant in low-frequency systems.

Question 29

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

Accepted Answer

4 J

Answer

2 J

Answer

10 J

Answer

20 J

Question 30

A rigid body is subjected to a constant force. Consequently, its:

Accepted Answer

Acceleration remains constant.

Answer

Velocity is always perpendicular to the applied force.

Answer

Kinetic energy is directly proportional to the elapsed time.

Answer

Potential energy decreases with time.

Question 31

A rigid body undergoes rotation about a fixed axis with a constant angular velocity. Which of the following quantities remains constant during this motion?

Accepted Answer

Angular momentum

Answer

Kinetic energy

Answer

Linear momentum

Answer

Potential energy

Question 32

A particle travels along a circular path of radius 'r' with a constant speed 'v'. Determine the centripetal force acting on the particle.

Accepted Answer

mv^2/r

Answer

mv^2

Answer

mr^2v

Answer

mr^2v^2

Question 33

Which of the following is a scalar quantity?

Accepted Answer

Displacement

Answer

Velocity

Answer

Acceleration

Answer

Force

Question 34

A particle is in motion with a constant velocity. Which of the following is zero?

Accepted Answer

Acceleration

Answer

Displacement

Answer

Momentum

Answer

Kinetic energy

Question 35

Identify the unit of impulse.

Accepted Answer

Newton-second

Answer

Newton-meter

Answer

Joule

Answer

Kilogram-meter per second

Question 36

A force of 100 N is applied to a mass of 20 kg resting on a frictionless surface. Calculate the acceleration produced.

Accepted Answer

2 m/s²

Answer

5 m/s²

Answer

10 m/s²

Answer

20 m/s²

Question 37

A simple pendulum of length 1 m oscillates with a period of 2 seconds. Determine the acceleration due to gravity at the location.

Accepted Answer

9.8 m/s²

Answer

19.6 m/s²

Answer

39.2 m/s²

Answer

58.8 m/s²

Question 38

A particle moves with a constant velocity of 10 m/s in the positive x-direction. What is its displacement after 5 seconds?

Accepted Answer

50 meters

Answer

25 meters

Answer

10 meters

Answer

100 meters

Question 39

A block of mass 10 kg is pushed along a horizontal surface with a force of 20 N. If the coefficient of kinetic friction between the block and the surface is 0.2, what is the acceleration of the block?

Accepted Answer

1.6 m/s²

Answer

3.2 m/s²

Answer

0.8 m/s²

Answer

2.4 m/s²

Question 40

A car is traveling around a curve of radius 100 m at a constant speed of 20 m/s. What is the centripetal force acting on the car?

Accepted Answer

400 Newtons

Answer

200 Newtons

Answer

600 Newtons

Answer

800 Newtons

Question 41

A flywheel of mass 100 kg and radius 0.5 m is rotating at 600 rpm. What is its angular momentum?

Accepted Answer

600 kg m²/s

Answer

900 kg m²/s

Answer

1200 kg m²/s

Answer

300 kg m²/s

Question 42

A system of two rigid bodies is in equilibrium under the action of three forces. What is the condition for equilibrium?

Accepted Answer

The net force and the net torque acting on the system are both zero.

Answer

The net force acting on the system is zero.

Answer

The net torque acting on the system is zero.

Question 43

In a work-energy problem, which of the following is NOT a type of energy that can be involved?

Accepted Answer

Sound energy

Answer

Thermal energy

Answer

Potential energy

Answer

Kinetic energy

Question 44

The angular momentum of a rotating object is conserved when:

Accepted Answer

No external torque acts on the object, and its mass distribution does not change.

Answer

The object's mass is constant.

Answer

The object's radius is constant.

Answer

The object's velocity is constant.

Question 45

In a collision between two objects, which of the following quantities is NOT conserved for the system of the two objects?

Accepted Answer

Kinetic energy

Answer

Total Energy

Answer

Angular momentum

Answer

Momentum

Question 46

In the context of dynamics, which of the following is a scalar quantity?

Accepted Answer

Time

Answer

Acceleration

Answer

Force

Answer

Velocity

Question 47

A rigid body rotates about a fixed axis with a constant angular velocity. Which of the following statements about the kinetic energy of the body is true?

Accepted Answer

It is proportional to the square of the angular velocity.

Answer

It is inversely proportional to the angular velocity.

Answer

It is independent of the angular velocity.

Question 48

A rigid body is subjected to a force that produces a moment about a fixed point. Which of the following will not affect the angular acceleration of the body?

Accepted Answer

Mass of the body

Answer

Distance from the point to the line of action of the force

Answer

Direction of the force

Answer

Magnitude of the force

Question 49

A car travels around a curve of radius R at a constant speed v. What is the car's centripetal acceleration?

Accepted Answer

v^2 / R

Answer

2v / R

Answer

v^2 / 2R

Answer

v / R

Question 50

A pendulum of length L oscillates with an amplitude of θ0. What is the pendulum's maximum velocity?

Accepted Answer

√(gL) * θ0

Answer

g * L * θ0

Answer

g * θ0 / L

Answer

√(gL) * θ0^2

Question 51

A spring with spring constant k is stretched by a distance x. What potential energy is stored in the spring?

Accepted Answer

1/2 * k * x^2

Answer

k * x

Answer

2 * k * x^2

Answer

1/4 * k * x^2

Question 52

A block slides down a frictionless inclined plane. What is the block's acceleration?

Accepted Answer

g * sinθ

Answer

0

Answer

g * cosθ

Answer

g

Question 53

A rigid body rotates about a fixed axis with an angular velocity of ω. What is the body's kinetic energy?

Accepted Answer

1/2 * I * ω^2

Answer

I * ω

Answer

1/4 * I * ω^2

Answer

2 * I * ω^2

Question 54

A particle moves along a straight line with its velocity increasing at a constant rate. This indicates that the particle is undergoing:

Accepted Answer

Uniform acceleration

Answer

Uniform deceleration

Answer

Periodic acceleration

Answer

Zero acceleration

Question 55

A block of mass 'm' is attached to a spring with a spring constant 'k'. The block is pulled to a displacement 'A' from its equilibrium position and released. What is the maximum acceleration experienced by the block during its subsequent motion?

Accepted Answer

kA/m

Answer

Zero

Answer

2kA/m

Answer

kA/2m

Question 56

A particle moves in a circular path of radius 'r' with a constant speed 'v'. What is the angular velocity of the particle?

Accepted Answer

v/r

Answer

v^2/r

Answer

r^2/v

Answer

rv

Question 57

A ball is thrown vertically upwards with an initial velocity 'u'. What is the maximum height reached by the ball?

Accepted Answer

(u^2)/(2g)

Answer

u^2/g

Answer

2gu^2

Answer

g/u^2

Question 58

A car of mass 'm' is traveling at a constant speed 'v' when the brakes are applied, causing a braking force 'F'. How far does the car travel before coming to rest?

Accepted Answer

(mv^2)/(2F)

Answer

2(mv^2)/F

Answer

(mv^2)/F

Answer

F(mv^2)/2

Question 59

Work 'W' is done on a system. If the potential energy of the system increases by 'U' and the kinetic energy increases by 'K', which equation correctly relates these quantities?

Accepted Answer

W = U + K

Answer

K = W - U

Answer

U = W - K

Answer

W = U - K

Question 60

A ball is thrown vertically upwards with an initial velocity 'u'. What is the power developed by gravity at the highest point of the ball's trajectory?

Accepted Answer

Zero

Answer

Positive

Answer

Negative

Answer

Maximum

Question 61

A machine has a mechanical advantage of 'MA'. If the efficiency of the machine is 'η', what is the ratio of output force to input force?

Accepted Answer

η * MA

Answer

η / MA

Answer

MA^2 * η

Answer

MA / η

Question 62

A 10 kg mass is moving at a constant velocity of 5 m/s. What is the net force acting on the mass?

Accepted Answer

0 N

Answer

2 N

Answer

10 N

Answer

50 N

Question 63

A car accelerates from rest to 20 m/s in 5 seconds. What is the car's acceleration?

Accepted Answer

4 m/s²

Answer

25 m/s²

Answer

100 m/s²

Answer

1 m/s²

Question 64

A 50 kg box is pushed across a horizontal floor with a force of 100 N. If the coefficient of kinetic friction between the box and the floor is 0.2, what is the acceleration of the box?

Accepted Answer

1 m/s²

Answer

2 m/s²

Answer

10 m/s²

Answer

5 m/s²