Dynamics for Engineering Mechanics: Master Motion and Forces

Question 1

A particle moves in a straight line with an acceleration given by a(t) = 2t + 3. If its initial velocity is v0 = 5 m/s, what is its velocity at time t = 2 s?

Accepted Answer

v = 11 m/s

Answer

v = 7 m/s

Answer

v = 15 m/s

Answer

v = 19 m/s

Question 2

When a person on a skateboard pushes against a stationary wall, what force does the wall exert on the person, according to Newton's third law?

Accepted Answer

Equal in magnitude and opposite in direction to the force applied by the person

Answer

Greater than the force applied by the person

Answer

Perpendicular to the force applied by the person

Answer

Newton's third law does not apply here

Question 3

A force of 100 N is applied to a body of mass 20 kg. Determine its acceleration according to Newton's second law.

Accepted Answer

10 m/s^2

Answer

5 m/s^2

Answer

20 m/s^2

Answer

50 m/s^2

Question 4

A particle moves along a straight line with an acceleration given by a(t) = 2t - 5. If its initial velocity at t = 0 is 3 m/s, determine its velocity at t = 2 s.

Accepted Answer

7 m/s

Answer

1 m/s

Answer

3 m/s

Answer

5 m/s

Question 5

A satellite of mass 500 kg orbits Earth in a circular path with a radius of 6370 km. Calculate its orbital velocity.

Accepted Answer

8.91 km/s

Answer

7.91 km/s

Answer

9.91 km/s

Answer

10.91 km/s

Question 6

A rigid body has a moment of inertia I about an axis that passes through its center of mass. If the body is subjected to a torque τ about the same axis, determine the resulting angular acceleration.

Accepted Answer

τ/I

Answer

I/τ

Answer

τ²I

Answer

I²τ

Question 7

The work done by a constant force F acting on a body through a displacement s is given by:

Accepted Answer

Fs

Answer

F/s

Answer

s/F

Answer

F²s

Question 8

Which of the following is considered a conservative force?

Accepted Answer

Gravity

Answer

Friction

Answer

Tension

Answer

Drag

Question 9

Which of the following is not one of Newton's Laws of Motion?

Accepted Answer

Hooke's Law

Answer

Newton's First Law

Answer

Newton's Second Law

Answer

Newton's Third Law

Question 10

A particle moves along a straight line, and its displacement (s) in meters at time (t) in seconds is given by the equation: s = 2t³ - 6t² + 3t. What is the particle's acceleration at t = 2 seconds?

Accepted Answer

18 m/s²

Answer

12 m/s²

Answer

6 m/s²

Answer

0 m/s²

Question 11

A particle starts from rest and accelerates uniformly at a rate of 'a' for a time 't'. The distance traveled by the particle in time 't' is:

Accepted Answer

ut + 1/2at^2

Answer

at^2

Answer

1/2(u + a)t

Answer

ut - 1/2at^2

Question 12

The kinetic energy of a body with mass 'm' moving with velocity 'v' is:

Accepted Answer

1/2mv^2

Answer

mv^2

Answer

2mv^2

Answer

1/4mv^2

Question 13

A projectile is launched with an initial velocity 'v' at an angle 'θ' above the horizontal. The maximum height reached by the projectile is:

Accepted Answer

v^2sin^2θ / 2g

Answer

v^2cos^2θ / 2g

Answer

v^2 / 2g

Answer

v^2tanθ / g

Question 14

Which of the following is the fundamental unit of force in the SI system?

Accepted Answer

Newton

Answer

Joule

Answer

Watt

Answer

Pascal

Question 15

A car of mass 'm' moves on a circular track of radius 'r' with a constant speed 'v'. The centripetal force acting on the car is:

Accepted Answer

mv^2 / r

Answer

2mv^2 / r

Answer

mv^2 / 2r

Answer

Zero

Question 16

Which of the following is an example of a non-conservative force?

Accepted Answer

Friction

Answer

Gravitational force

Answer

Elastic force

Answer

Electrostatic force

Question 17

The equation of motion for a damped harmonic oscillator is:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 18

A uniform disk with radius R and mass M rolls without slipping on a flat surface. Calculate its kinetic energy.

Accepted Answer

1/2 * MV^2 + 1/2 * MR^2 * ω^2

Answer

1/2 * MV^2

Answer

1/2 * MR^2 * ω^2

Answer

1/4 * MV^2

Question 19

A constant force of 100 N is applied to a 20 kg object initially at rest. Determine the object's kinetic energy after 5 seconds.

Accepted Answer

500 J

Answer

250 J

Answer

750 J

Answer

1000 J

Question 20

A car travels 100 km in 1 hour. Calculate the car's average speed in km/h.

Accepted Answer

60

Answer

50

Answer

70

Answer

80

Question 21

A rotating wheel has a radius of 0.5 m and an angular velocity of 10 rad/s. What is the wheel's tangential velocity?

Accepted Answer

5 m/s

Answer

2.5 m/s

Answer

7.5 m/s

Answer

10 m/s

Question 22

A particle moves in a straight line with a constant acceleration. Its velocity-time graph will be a:

Accepted Answer

Straight line inclined to the time axis

Answer

Straight line parallel to the time axis

Answer

Parabola

Answer

Hyperbola

Question 23

A body of mass 'm' is moving with a velocity 'v'. The kinetic energy of the body is:

Accepted Answer

mv^2/2

Answer

mv

Answer

mv^2

Answer

2mv

Question 24

Which of the following is NOT a conservative force?

Accepted Answer

Frictional force

Answer

Gravitational force

Answer

Spring force

Answer

Electrostatic force

Question 25

A rigid body is in equilibrium under the action of a system of forces. The resultant of these forces is:

Accepted Answer

Zero

Answer

Non-zero

Answer

Parallel to the resultant of the moments of the forces

Answer

Perpendicular to the resultant of the moments of the forces

Question 26

A beam of length 'L' is supported at both ends. The maximum bending moment occurs at:

Accepted Answer

Mid-span

Answer

Supports

Answer

Quarter-span

Answer

Third-span

Question 27

The natural frequency of a mass-spring system is:

Accepted Answer

√(k/m)

Answer

√(m/k)

Answer

k/m

Answer

m/k

Question 28

The damping ratio of a system is a measure of its:

Accepted Answer

Damping

Answer

Stiffness

Answer

Frequency

Answer

Mass

Question 29

A rigid body rotates about a fixed axis with an initial angular velocity of 10 rad/s. If its angular acceleration is 2 rad/s², what is its angular displacement after 5 seconds?

Accepted Answer

50 rad

Answer

25 rad

Answer

75 rad

Answer

100 rad

Question 30

Which of the following is not a conservative force?

Accepted Answer

Friction

Answer

Gravity

Answer

Centripetal force

Answer

Magnetic force

Question 31

A machine has an efficiency of 75%. If the input power is 100 W, what is the output power?

Accepted Answer

75 W

Answer

25 W

Answer

50 W

Answer

100 W

Question 32

A particle moves in a circular path of radius 'r' with a constant speed 'v'. The magnitude of its acceleration is:

Accepted Answer

v/r (centripetal acceleration)

Answer

v^2/r

Answer

zero

Answer

rv^2

Question 33

A body of mass 'm' is moving with velocity 'u'. A force 'F' acts on the body for time 't' and changes its velocity to 'v'. The work done by the force 'F' is:

Accepted Answer

1/2 * m(v^2 - u^2)

Answer

m(v - u)

Answer

m(v^2 + u^2)/2

Answer

m(v - u)t

Question 34

A particle is projected vertically upwards with velocity 'u'. The maximum height reached by the particle is:

Accepted Answer

u^2/(2g)

Answer

u/g

Answer

2u^2/g

Answer

g/u^2

Question 35

A body is moving on a horizontal surface with a constant velocity. The work done by the force of friction is:

Accepted Answer

Zero

Answer

Positive

Answer

Negative

Answer

Depends on the direction of motion

Question 36

A system of pulleys is arranged to lift a weight 'W'. If the velocity ratio of the system is 'n', then the effort required to lift the weight is:

Accepted Answer

W/n

Answer

nW

Answer

W/2n

Answer

2nW

Question 37

A body is rotating about a fixed axis. The angular momentum of the body is:

Accepted Answer

Proportional to its both angular velocity and moment of inertia

Answer

Proportional to its angular velocity

Answer

Proportional to its moment of inertia

Answer

Inversely proportional to its both angular velocity and moment of inertia

Question 38

In a simple harmonic motion, the displacement of the particle from its mean position is given by the equation x = Acos(ωt + φ). The amplitude of the motion is:

Accepted Answer

A

Answer

ω

Answer

φ

Answer

Aω

Question 39

A particle moves along a straight line with constant acceleration. Which graph best represents the relationship between its velocity and time?

Accepted Answer

A straight line with a positive slope

Answer

A straight line with a negative slope

Answer

A parabola opening upward

Answer

A parabola opening downward

Question 40

A block slides down a frictionless inclined plane. Which statement accurately describes its motion?

Accepted Answer

It accelerates uniformly.

Answer

It decelerates uniformly.

Answer

Its acceleration increases as it slides down.

Answer

Its acceleration decreases as it slides down.

Question 41

A system is considered conservative if:

Accepted Answer

Its total energy remains constant.

Answer

Its momentum remains constant.

Answer

Its work done on the surroundings is zero.

Answer

Its heat transfer with the surroundings is zero.

Question 42

Which of the following is an example of a non-conservative force?

Accepted Answer

Friction

Answer

Gravity

Answer

Tension

Answer

Normal force

Question 43

Which statement is true about impact?

Accepted Answer

It conserves momentum but not kinetic energy.

Answer

It is always an elastic collision.

Answer

It is always an inelastic collision.

Answer

It conserves both momentum and kinetic energy.

Question 44

The work done by a force is path-independent if the force is:

Accepted Answer

Conservative

Answer

Non-conservative

Answer

Frictional

Answer

Gravitational

Question 45

Which of the following is the angular momentum of a particle of mass m moving in a circular path of radius r with a speed v?

Accepted Answer

mrv

Answer

2mrv

Answer

4mrv

Answer

8mrv

Question 46

A rocket engine provides a constant thrust of 1000 N for 10 seconds. The change in momentum of the rocket during this period will be:

Accepted Answer

10000 kg-m/s

Answer

5000 kg-m/s

Answer

15000 kg-m/s

Answer

20000 kg-m/s

Question 47

A particle moves in a straight line with constant acceleration (a). It starts from rest and covers a distance (s) in time (t). Which of the following equations correctly describes the motion ?

Accepted Answer

s = 0.5 * a * t^2

Answer

s = 2 * a * t

Answer

s = 0.25 * a * t^2

Answer

s = a * t

Question 48

A force (F) is applied to a body of mass (m) that is initially at rest. The work done (W) by the force in moving the body through a displacement (d) is given by:

Accepted Answer

W = F * d

Answer

W = 0.5 * F * d

Answer

W = 2 * F * d

Answer

W = F * d^2

Question 49

A flywheel of moment of inertia (I) is rotating with an angular velocity (ω). The kinetic energy (K) of the flywheel is:

Accepted Answer

K = 0.5 * I * ω^2

Answer

K = 2 * I * ω^2

Answer

K = I * ω

Answer

K = 0.25 * I * ω^2

Question 50

In a simple Atwood machine, two masses (m1 and m2) are connected by a light inextensible string passing over a frictionless pulley. When released from rest:

Accepted Answer

The acceleration of the system is g * (m1 - m2) / (m1 + m2)

Answer

The acceleration of the system is g

Answer

The acceleration of the system is g * (m1 + m2) / (m1 - m2)

Answer

The acceleration of the system is zero

Question 51

A spring-mass system consists of a mass (m) attached to a spring with spring constant (k). When the mass is displaced from its equilibrium position by a distance (x) and released, the maximum velocity (v) of the mass is:

Accepted Answer

v = √(k / m) * x

Answer

v = √(m / k) * x

Answer

v = m / k * x

Answer

v = k / m * x

Question 52

A circular disc of radius (r) is rotating about its axis with an angular velocity (ω). The kinetic energy (K) of the disc is:

Accepted Answer

K = 0.5 * m * r^2 * ω^2

Answer

K = 0.25 * m * r^2 * ω^2

Answer

K = m * r^2 * ω

Question 53

A body of mass 'm' is moving with a velocity 'v'. The kinetic energy of the body is given by:

Accepted Answer

(1/2)mv^2

Answer

v^2/m

Answer

mv

Answer

m^2v

Question 54

The moment of inertia of a body about an axis depends on:

Accepted Answer

Mass distribution of the body and the choice of axis

Answer

Shape of the body only

Answer

Mass of the body only

Question 55

A rigid body is rotating about a fixed axis with constant angular velocity. The angular acceleration of the body is:

Accepted Answer

Zero

Answer

Cannot be determined without additional information

Answer

Non-zero and variable

Answer

Non-zero and constant

Question 56

The work-energy theorem states that:

Accepted Answer

The net work done on a system is equal to the change in its kinetic energy

Answer

The net work done on a system is equal to the change in its internal energy

Answer

The net work done on a system is equal to the change in its potential energy

Question 57

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

Accepted Answer

4 m/s²

Answer

100 m/s²

Answer

1 m/s²

Answer

0.25 m/s²

Question 58

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

Accepted Answer

0 N

Answer

50 N

Answer

10 N

Answer

5 N

Question 59

A 5 kg block is pulled horizontally across a frictionless surface with a force of 20 N. What is the acceleration of the block?

Accepted Answer

4 m/s²

Answer

1 m/s²

Answer

100 m/s²

Question 60

A 2 kg ball is thrown vertically upwards with an initial velocity of 10 m/s. What is the maximum height reached by the ball?

Accepted Answer

5.1 m

Answer

10 m

Answer

20 m

Answer

1 m

Question 61

A 10 kg box is sliding down a 30° incline with a coefficient of friction of 0.2. What is the acceleration of the box?

Accepted Answer

3.1 m/s²

Answer

9.8 m/s²

Answer

5.88 m/s²

Answer

1.96 m/s²

Question 62

A 5 kg object is moving with a velocity of 4 m/s. What is the kinetic energy of the object?

Accepted Answer

40 J

Answer

80 J

Answer

20 J

Answer

10 J

Question 63

A force of 10 N is applied to move a 2 kg object over a distance of 5 m. What is the work done by the force?

Accepted Answer

50 J

Answer

10 J

Answer

100 J

Answer

20 J

Question 64

A 10 kg object is raised vertically 2 meters. What is the potential energy gained by the object?

Accepted Answer

196 J

Answer

98 J

Answer

49 J

Answer

392 J