Free Printable 13/01/2026 AE: EM-SHM, LIFTING MACHINES, CG AND MOI

Worksheets

13/01/2026 AE: EM-SHM, LIFTING MACHINES, CG AND MOI

Total questions: 46

Worksheet time: 23mins

Name

Class

Date

The property of a beam section that indicates its resistance to bending and deflection is known as:

Mass Moment of Inertia

Center of Gravity

Area Moment of Inertia

Parallel Axis Theorem

Calculate the Area Moment of Inertia for a circular section with a diameter of 40 mm about its centroidal axis.

12566 mm^4

25133 $mm^4$

50265 $mm^4$

100530 mm^4

For a non-uniform material, such as reinforced concrete with steel, which statement is typically true?

The Center of Gravity and the Centroid are always at the same point.

The Centroid does not exist for such materials.

The Center of Gravity and the Centroid are not at the same point.

The location of the Center of Gravity depends only on geometry.

A thin rod of mass $M$ and length $L$ is rotating about an axis passing through its end and perpendicular to its length. What is its Mass Moment of Inertia?

$ML^2 / 12$

$ML^2 / 3$

$MR^2 / 2$

$\tfrac{2}{5} MR^2$

Evaluate the following statements regarding Moment of Inertia (MOI). Which statement is correct?

Area MOI is a physical property used in Dynamics to analyze rotation.

Mass MOI is a geometric property used in Strength of Materials to analyze bending.

A larger Area MOI indicates a beam is less stiff and more prone to deflection.

Area MOI is a geometric property that represents a body's resistance to bending.

For a T-section with a centroid located at $ȳ = 8 cm$ from the base, a rectangular web section has its own centroid at $y1 = 5 cm$ . The area of the web is $20 cm^2$ . Calculate the web's contribution to the total MOI about the composite centroidal axis.

166.67 cm^4

180.00 cm^4

346.67 cm^4

$533.34 cm^4$

The centroid of a hollow cone of height H is located at what distance from its base?

H/4

H/3

3R/8

R/2

A solid sphere has a mass $M$ and radius $R$ . Its mass moment of inertia is:

$\tfrac{2}{3} MR^2$

$MR^2 / 2$

$ML^2 / 12$

$\tfrac{2}{5} MR^2$

What is the Area Moment of Inertia of a triangular section of base $b$ and height $h$ about an axis passing through its centroid and parallel to the base?

$bh^3 / 3$

$bh^3 / 12$

$bh^3 / 36$

$bh^3 / 12$

10.

What is the centroid of a standard semi-circular area of radius $R$ , measured from its diametral base?

$\tfrac{4R}{3\pi}$

$\tfrac{3R}{8}$

$\tfrac{R}{2}$

$\tfrac{2R}{\pi}$

11.

The dimension that is always cubed in the standard Area Moment of Inertia formulas for rectangular and triangular sections is:

The dimension parallel to the axis of rotation.

The dimension perpendicular to the axis of rotation.

The smaller of the two dimensions.

The larger of the two dimensions.

12.

A vibrating system completes 20 cycles in 4 seconds. What is its frequency?

0.2 Hz

5 Hz

20 Hz

80 Hz

13.

Which of the following statements provides the most accurate distinction between periodic motion and Simple Harmonic Motion (SHM)?

All periodic motions are SHM, but not all SHM is periodic.

Periodic motion occurs in a straight line, while SHM occurs in a circle.

SHM is a specific type of periodic motion where acceleration is proportional to displacement from a fixed point and directed towards it.

There is no fundamental difference; the terms are interchangeable.

14.

In which type of vibration does the amplitude continuously decrease over time due to energy loss?

Forced Vibration

Longitudinal Vibration

Damped Vibration

Free Vibration

15.

A "Second's Pendulum" is defined as a pendulum that has one beat per second. What is its time period (T)?

0.5 seconds

1.0 second

2.0 seconds

99.39 seconds

16.

Two springs with stiffness k1 = 300 N/m and k2 = 600 N/m are connected in series. What is the equivalent stiffness (ke) of the combination?

150 N/m

200 N/m

450 N/m

900 N/m

17.

The motion of plucked guitar strings is a classic example of which type of vibration?

Longitudinal Vibration

Torsional Vibration

Transverse Vibration

Damped Vibration

18.

A spring has a stiffness of 50 N/mm. What force is required to produce a deflection of 10 mm?

5 N

50 N

500 N

5000 N

19.

Identify the correct statement regarding the time period of a simple pendulum.

It is dependent on the mass of the pendulum's bob.

It is dependent on the length of the string.

It decreases as the length of the string increases.

It is dependent on the amplitude of the swing, regardless of its size.

20.

The instantaneous displacement 'x' of a body in SHM is given by $x = r \cos(\omega t)$ . At what point is the acceleration maximum?

At the mean position ( $x = 0$ )

At the extreme positions ( $x = \pm r$ )

When velocity is maximum

At all points, acceleration is constant

21.

If two springs with stiffness k1 and k2 are connected in parallel, how is the total load (W) distributed?

The load is the same in each spring.

The total load is the sum of the loads carried by individual springs.

The first spring takes the entire load.

The load is distributed inversely proportional to the stiffness.

22.

What is the frequency of a spring-mass system with a time period of 0.25 seconds?

0.25 Hz

2 Hz

4 Hz

8 Hz

23.

Which pendulum type is specifically used experimentally to determine the moment of inertia of a body?

Simple Pendulum

Second's Pendulum

Compound Pendulum

Torsional Pendulum

24.

A lifting machine raises a load of 1500 N with an effort of 50 N. What is the Mechanical Advantage (M.A.) of the machine?

1500

25.

In a lifting machine, the effort moves a distance of 10 m while the load moves 0.5 m. What is the Velocity Ratio (V.R.)?

0.05

10.5

26.

Which of the following statements accurately describes a reversible machine?

A machine with an efficiency of exactly 100%.

A machine with an efficiency less than 50%.

A machine where the load will start to move down if the effort is removed.

A machine that cannot do work in the opposite direction.

27.

The law of a machine is given by the equation $P = 0.05W + 20$ , where P is the effort and W is the load, both in Newtons. What is the maximum Mechanical Advantage of this machine?

0.05

28.

In which class of lever is the load located between the fulcrum and the effort?

Class 1 Lever

Class 2 Lever

Class 3 Lever

Compound Lever

29.

What is the Velocity Ratio of a first-order pulley system with 3 movable pulleys?

30.

A machine has a Velocity Ratio of 40 and a Mechanical Advantage of 32. Calculate its efficiency.

64%

72%

80%

125%

31.

Evaluate the following statements about machine characteristics. Which statement is false?

In an ideal machine, the output is equal to the input.

For an irreversible machine, the efficiency is less than 50%.

The term 'c' in the law of a machine P = mW + c represents the effort required to lift the load without friction.

A screw jack is a common example of an irreversible or self-locking machine.

32.

The Mechanical Advantage of a lever is also known as its:

Leverage

Fulcrum

Velocity Ratio

Efficiency

33.

What is the Velocity Ratio of an inclined plane where the angle of inclination is 30°?

0.5

1.0

1.732

2.0

34.

In a third-order pulley system with a total of 4 pulleys, what is the Velocity Ratio?

35.

A machine requires an effort of 200 N to lift a load of 5000 N. The Velocity Ratio of the machine is 30. Calculate the effort lost in friction.

33.3 N

166.7 N

200 N

233.3 N

36.

The principle of a lever is based on:

The conservation of energy.

The principle of moments.

Newton's second law of motion.

The efficiency of the machine.

37.

Consider a T-section with a flange of 80mm x 10mm and a web of 100mm x 10mm. The centroidal axis (Ixx) is $1.05 \times 10^6 mm^4$ . If we want to find the MOI about the base of the web using the Parallel Axis Theorem, what value of 'h' should be used? The centroid ȳ is $87.5 mm$ from the base.

10 mm

87.5 mm

100 mm

110 mm

38.

Which statement correctly identifies the condition for an ideal machine?

Its efficiency is greater than 50% but less than 100%.

The load lost in friction is equal to the actual load.

The Mechanical Advantage is equal to the Velocity Ratio.

It is always a self-locking machine.

39.

A mass 'm' is attached to two springs in parallel, with stiffness k1 and k2. What is the time period of oscillation?

$T = 2\pi\sqrt{m / (k_1 + k_2)}$

$T = 2\pi\sqrt{m \cdot (k_1 + k_2) / (k_1 k_2)}$

$T = 2\pi\sqrt{m / k_1} + 2\pi\sqrt{m / k_2}$

$T = 2\pi\sqrt{m \cdot (k_1 + k_2)}$

40.

For a solid cone of height H and a hollow hemisphere of radius R, where are their respective centroids located from their bases?

Cone at $H/3$ , Hemisphere at $R/2$

Cone at $H/4$ , Hemisphere at $3R/8$

Cone at $H/3$ , Hemisphere at $3R/8$

Cone at $H/4$ , Hemisphere at $R/2$

41.

A screw jack has a handle of length 40 cm and a screw pitch of 5 mm. What is its Velocity Ratio?

100.5

251.3

502.6

800

42.

Which of these descriptions matches a Class 3 Lever?

A curved lever bent at 90°, used in railway signals.

A lever where the fulcrum is between the load and effort, like scissors.

A lever where the effort is applied between the fulcrum and the load, like tweezers.

A lever where the load arm is always shorter than the effort arm.

43.

A machine has a V.R. of 50. An effort of 100 N is applied to lift a load "W". If the efficiency is 70%, what is the value of the load "W"?

35 N

350 N

3500 N

5000 N

44.

Identify the true statement regarding different types of vibrations.

In longitudinal vibration, particle displacement is perpendicular to the body's axis.

Forced vibration occurs when an initial excitation force is applied and then removed.

Torsional vibration involves an angular, twisting displacement around an axis.

Damped vibration is a theoretical case where energy losses are ignored.

45.

An effort of 50 N is applied to a lever to lift a load of 200 N. The fulcrum is located 20 cm from the load. What is the length of the effort arm?

5 cm

20 cm

40 cm

80 cm

46.

What is the fundamental condition for a body to exhibit Simple Harmonic Motion (SHM)?

The restoring force must be constant.

The velocity must be proportional to the displacement.

The acceleration must be proportional to the displacement and directed towards the equilibrium position.

The body must move in a circular path at a constant speed.

100 %

13/01/2026 AE: EM-SHM, LIFTING MACHINES, CG AND MOI

Total questions: 46

Worksheet time: 23mins

Similar Resources on Wayground