Dynamics of Bodies: Master Engineering Mechanics with Online Quizzes

Question 1

A particle of mass m moves in a circular path of radius r with a constant speed v. Determine the magnitude of the force acting on the particle.

Accepted Answer

mv²/r

Answer

mv/r

Answer

mr²/v

Answer

mrv

Question 2

A particle with a mass of 5 kg is initially at rest. A force described by F(t) = (3t + 2) N is applied to the particle for 10 seconds. Determine its velocity after this time.

Accepted Answer

70 m/s

Answer

65 m/s

Answer

90 m/s

Answer

110 m/s

Question 3

Summarize Newton's first law of motion, also known as the law of inertia.

Accepted Answer

An object at rest stays at rest, and an object in motion stays in motion with constant velocity unless acted upon by an external force.

Answer

The acceleration of an object is proportional to the force applied to it.

Answer

Objects resist changes in their motion due to inertia.

Answer

The mass of an object determines its velocity.

Question 4

According to Newton's third law of motion, when object A exerts a force on object B, what is the nature of the force exerted by object B on object A?

Accepted Answer

Equal in magnitude and opposite in direction

Answer

Greater in magnitude and opposite in direction

Answer

Equal in magnitude and in the same direction

Question 5

According to Newton's second law, when a net external force acts on a free-moving rigid object, the object will experience:

Accepted Answer

Acceleration

Answer

Displacement

Answer

Velocity

Answer

Angular displacement

Question 6

For a particle moving in a straight line with constant acceleration, which graph accurately depicts the relationship between its velocity and displacement?

Accepted Answer

A straight line with a positive slope passing through the origin

Answer

An upward-opening parabola

Answer

A circle

Question 7

A particle is moving along a curved path. Describe the relationship between the particle's velocity and acceleration vectors at any point on the path.

Accepted Answer

The tangential component of acceleration changes the particle's speed, while the normal component changes the direction of its velocity.

Answer

The velocity vector is always perpendicular to the acceleration vector.

Answer

The acceleration vector is always parallel to the path of motion.

Question 8

A rigid body is initially at rest and subjected to a force F and a torque τ. What type of motion will the body undergo?

Accepted Answer

Both translational and rotational motion

Answer

Translational motion only

Answer

Rotational motion only

Answer

No motion

Question 9

Analyze the motion of a spring-mass system subjected to a damping force proportional to its velocity. Explain how the damping coefficient influences the system's behavior.

Accepted Answer

The motion is periodic, with exponentially decreasing amplitude and constant frequency.

Answer

The motion is aperiodic, with amplitude increasing exponentially to infinity.

Answer

The damping force increases the system's natural frequency.

Answer

The system's total energy increases due to the damping force.

Question 10

Which of the following is **not** a fundamental type of force in physics?

Accepted Answer

Thermal force

Answer

Contact force

Answer

Gravitational force

Answer

Magnetic force

Question 11

Newton's second law of motion states that the acceleration of an object is directly proportional to its:

Accepted Answer

Mass and force

Answer

Mass only

Answer

Force only

Answer

Force and acceleration

Question 12

What is the SI unit of momentum?

Accepted Answer

Kilogram meters per second (kg m/s)

Answer

Newton meters (N m)

Answer

Kilograms per second (kg/s)

Answer

Newtons (N)

Question 13

Which of the following is **not** a factor that influences the trajectory of a projectile?

Accepted Answer

Object's shape

Answer

Initial velocity

Answer

Acceleration due to gravity

Answer

Air resistance

Question 14

Which of the following is a conservative force?

Accepted Answer

Gravity

Answer

Friction

Answer

Tension

Answer

Air resistance

Question 15

Which of the following is used to describe the pure rotational motion of a rigid body?

Accepted Answer

Angular displacement and velocity

Answer

Linear displacement and velocity

Answer

Linear and angular displacement

Answer

Linear and angular velocity

Question 16

Identify the non-conservative force among the following:

Accepted Answer

Frictional force

Answer

Gravitational force

Answer

Elastic force

Answer

Tension force

Question 17

Which expression accurately represents the centripetal acceleration of a body traversing a circular path?

Accepted Answer

a = v^2/r

Answer

a = v/r

Answer

a = r/v

Answer

a = r*v

Question 18

A rigid body rotates around a fixed axis with an angular velocity of 10 radians per second. Calculate its angular displacement after 5 seconds.

Accepted Answer

50 rad

Answer

25 rad

Answer

75 rad

Answer

100 rad

Question 19

Which expression correctly defines the power generated by a force?

Accepted Answer

P = Fv

Answer

P = F/v

Answer

P = v/F

Answer

P = F^2/v

Question 20

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

mv²/r (centripetal force)

Answer

mv/r (tangential force)

Answer

Zero

Answer

2mv²/r

Question 21

A projectile is launched from the ground with a velocity of 20 m/s at an angle of 30° above the horizontal. What is the maximum height reached by the projectile?

Accepted Answer

15.3 m (correct)

Answer

10.2 m

Answer

5.1 m

Answer

20.4 m

Question 22

A uniform rod of length 'L' and mass 'M' is pivoted at one end. A force 'F' is applied perpendicular to the rod at a distance 2L/3 from the pivot. What is the angular acceleration of the rod?

Accepted Answer

2F/(3ML) (correct)

Answer

3F/(2ML)

Answer

3F/(ML)

Answer

2F/(5ML)

Question 23

A flywheel of mass 200 kg has a radius of gyration of 1 m. If the flywheel rotates at 100 rad/s, what is its kinetic energy?

Accepted Answer

100 kJ (correct)

Answer

50 kJ

Answer

200 kJ

Answer

150 kJ

Question 24

A simple harmonic oscillator has a mass of 1 kg and a spring constant of 100 N/m. What is the period of oscillation?

Accepted Answer

2π s (correct)

Answer

π s

Answer

1 s

Answer

0.5 s

Question 25

A rigid body is subjected to a force of 100 N along the x-axis and a moment of 50 Nm about the z-axis. What are the net force and the net moment acting on the body?

Accepted Answer

100 N, 50 Nm (correct)

Answer

100 N, 0 Nm

Answer

0 N, 50 Nm

Answer

0 N, 0 Nm

Question 26

A beam with a length of 6 m is simply supported at both ends and carries a uniformly distributed load of 2 kN/m. What is the maximum bending moment?

Accepted Answer

12 kNm (correct)

Answer

6 kNm

Answer

3 kNm

Answer

9 kNm

Question 27

A truss is analyzed using the method of joints. The reactions at the supports are found to be A: 10 kN, B: 5 kN, and C: 0 kN. What is the force in the member BC?

Accepted Answer

10 kN (correct)

Answer

5 kN

Answer

15 kN

Answer

0 kN

Question 28

A simply supported beam of length L is subjected to a uniformly distributed load of w N/m. What is the maximum bending moment?

Accepted Answer

wL²/8

Answer

wL²/4

Answer

wL²/2

Answer

wL²

Question 29

A particle moving with constant velocity has a net force acting on it. True or False?

Accepted Answer

False

Answer

True

Question 30

Which of the following is NOT a vector quantity?

Accepted Answer

Speed

Answer

Velocity

Answer

Displacement

Answer

Acceleration

Question 31

A particle moves in a straight line with constant acceleration. Which of the following graphs represents its velocity-time relationship?

Accepted Answer

A straight line with a positive slope

Answer

A straight line with a negative slope

Answer

A parabola

Answer

A circle

Question 32

Which of the following is a conservative force?

Accepted Answer

Gravity

Answer

Friction

Answer

Tension

Answer

Magnetic force

Question 33

A particle is projected vertically upward with a velocity of 10 m/s. What is the maximum height it will reach?

Accepted Answer

10 m

Answer

5 m

Answer

15 m

Answer

20 m

Question 34

A system is in equilibrium when both the net force and the net torque acting on it are zero.

Accepted Answer

True

Answer

False

Question 35

Which of the following forces does NOT act on a body?

Accepted Answer

Weak nuclear force

Answer

Contact force

Answer

Gravitational force

Answer

Electromagnetic force

Question 36

Which condition is NOT necessary for a body to be in equilibrium?

Accepted Answer

Zero displacement of the body

Answer

Zero net force acting on the body

Answer

Zero net torque acting on the body

Answer

Zero acceleration of the body

Question 37

A machine has an efficiency of 80%. If the input work is 100 J, what is the output work?

Accepted Answer

80 J

Answer

20 J

Answer

60 J

Answer

100 J

Question 38

Which equation correctly defines the power of a force?

Accepted Answer

P = Ft

Answer

P = F/t

Answer

P = t/F

Answer

P = F²t

Question 39

Newton's second law of motion establishes the relationship between force, mass, and acceleration. Accurately state the law:

Accepted Answer

The acceleration of an object is directly proportional to the net force acting on the object.

Answer

The acceleration of an object is directly proportional to the mass of the object.

Answer

The acceleration of an object is inversely proportional to the mass of the object.

Answer

The acceleration of an object is inversely proportional to the net force acting on the object.

Question 40

Kinetic energy is the energy possessed by an object due to its motion. Which of the following formulas correctly represents kinetic energy?

Accepted Answer

E = 1/2 mv^2

Answer

E = mc^2

Answer

E = Fd

Answer

E = mgh

Question 41

A simple pendulum is a weight suspended from a fixed point by a string. Determine the natural frequency of a simple pendulum:

Accepted Answer

f = (1/2π)√(g/L)

Answer

f = (1/π)√(g/L)

Answer

f = (2π)√(g/L)

Answer

f = π√(g/L)

Question 42

A particle moves in a straight line with constant acceleration. Which graph below represents the velocity-time relationship for this motion?

Accepted Answer

A straight line with a positive slope

Answer

A straight line with a negative slope

Answer

A parabola

Answer

A hyperbola

Question 43

A body of mass 'm' is launched vertically upwards with an initial velocity 'v'. What is the maximum height reached by the body?

Accepted Answer

v^2/2g

Answer

v^2/g

Answer

2v^2/g

Answer

g^2/2v

Question 44

What is the moment of inertia of a solid cylinder about its axis of symmetry?

Accepted Answer

mr^2/4

Answer

mr^2/2

Answer

3mr^2/4

Answer

mr^2

Question 45

Which of the following is a necessary condition for equilibrium of a rigid body?

Accepted Answer

Both the net force and the net torque on the body are zero.

Answer

The net force on the body is zero.

Answer

The net torque on the body is zero.

Answer

Neither the net force nor the net torque on the body is zero.

Question 46

What is the principle of virtual work used for?

Accepted Answer

Determining the forces acting on a body

Answer

Calculating the displacement of a body

Answer

Finding the potential energy of a body

Answer

Analyzing the stability of a structure

Question 47

A body moves with a constant speed of 10 m/s. What is its acceleration?

Accepted Answer

0 m/s²

Answer

10 m/s²

Answer

Cannot be determined from the given information

Question 48

Which of the following is a dimensionless quantity?

Accepted Answer

Reynolds number

Answer

Force

Answer

Mass

Answer

Energy

Question 49

A fluid flows through a pipe with a varying velocity profile. What is the average velocity of the fluid?

Accepted Answer

Mean velocity

Answer

Maximum velocity

Answer

Minimum velocity

Answer

Root mean square velocity

Question 50

A force of 100 N is applied to a body with a mass of 20 kg for 5 seconds. What is the impulse imparted to the body?

Accepted Answer

200 Ns

Answer

20 Ns

Answer

100 Ns

Answer

500 Ns

Question 51

A particle has a velocity given by v(t) = 2t + 3 m/s. What is its acceleration?

Accepted Answer

2 m/s^2

Answer

3 m/s^2

Answer

5 m/s^2

Answer

10 m/s^2

Question 52

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

Accepted Answer

g sin θ - μk g cos θ

Answer

g cos θ - μk g sin θ

Answer

g sin θ + μk g cos θ

Answer

g cos θ + μk g sin θ

Question 53

A satellite of mass m orbits the Earth at a distance of r from its center. What is the centripetal force acting on it?

Accepted Answer

GmM/r^2

Answer

Gm^2/r

Answer

r^2/GmM

Answer

m^2/Gr

Question 54

When a body is in equilibrium under the action of three forces which of the following statements is true?

Accepted Answer

The sum of the forces is zero

Answer

The forces are equal in magnitude

Answer

The forces are parallel to each other

Answer

The forces are perpendicular to each other

Question 55

A simple harmonic oscillator has a frequency of 1 Hz. What is its period of oscillation?

Accepted Answer

1 s

Answer

0.5 s

Answer

2 s

Answer

4 s

Question 56

Which of the following is a conservative force?

Accepted Answer

Gravity

Answer

Friction

Answer

Tension

Answer

Air resistance

Question 57

A particle travels in a circular path at a constant speed. Which statement is true?

Accepted Answer

The particle has a constant acceleration toward the circle's center

Answer

The particle has no acceleration

Answer

The particle has a constant acceleration away from the circle's center

Answer

The particle has a variable acceleration

Question 58

A particle moves in a straight line with a constant velocity of 10 m/s. What displacement does the particle undergo in 5 seconds?

Accepted Answer

20 m

Answer

10 m

Answer

50 m

Answer

100 m

Question 59

Which of the following quantities is a vector?

Accepted Answer

Acceleration

Answer

Speed

Answer

Mass

Answer

Temperature

Question 60

A wheel rolls without slipping. Which statement describes the wheel's motion?

Accepted Answer

Linear and angular velocities are equal.

Answer

Linear velocity exceeds angular velocity.

Answer

Angular velocity exceeds linear velocity.

Answer

Both linear and angular velocities are zero.

Question 61

Which of the following is defined as a quantity that has both magnitude and direction?

Accepted Answer

Vector

Answer

Scalar

Answer

Tensor

Answer

Matrix

Question 62

Which of the following is the expression for the kinetic energy of a rotating body?

Accepted Answer

1/2 I ω²

Answer

I ω

Answer

1/2 I ω

Answer

I ω²

Question 63

Which of the following forces is considered conservative?

Accepted Answer

Gravity

Answer

Friction

Answer

Tension

Answer

Air resistance

Question 64

A body is in equilibrium if:

Accepted Answer

Both A and B are true

Answer

The net force acting on the body is zero

Answer

The net torque acting on the body is zero

Answer

Neither A nor B is true