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American System Physics

A Physics Toolkit

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Representing Motion

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Accelerated Motion

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Forces in One Dimension

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Displacement and Force in Two Dimensions

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Motion in Two Dimensions

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Gravitation

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Rotational Motion

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Momentum and Its Conservation

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Energy and Its Conservation

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Thermal Energy

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States of Matter

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Vibrations and Waves

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Sound

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Fundamentals of Light

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Reflection and Refraction

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Interference and Diffraction

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Electrostatics

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Electric Current and Circuits

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Magnetic Fields

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Electromagnetic Induction and Electromagnetism

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Quantum Theory and the Atom

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Solid-State Electronics

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Nuclear and Particle Physics

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Quiz

8.3 Equilibrium and Centre of Mass – Quiz

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Equilibrium and Centre of Mass American Physics quiz: free practice for American System Physics. Work through this Equilibrium and Centre of Mass American Physics quiz and get instant feedback on every answer. If you get stuck, review the 8.3 Equilibrium and Centre of Mass — Notes lesson. More practice: American System Physics — all units. Syllabus: OpenStax free science textbooks.

  • Questions count: 50
  • Passing grade: A-
  • Time limit:
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1.
Why do racing cars have low bodies and wide wheelbases?
To reduce their mass
A low centre of mass and wide base make them harder to tip over when cornering
To increase their moment of inertia about the wheel axle
To make the centrifugal force larger
2.
A student hangs a flat ring from holes P and Q and draws the plumb lines, which cross at X in the empty centre (diagram). She concludes the method has failed. Which evaluation is correct?
Dr Dabour Hub Academy - figure 1
The method worked: a ring's centre of mass is at its centre, even though no material is there
The method failed because the centre of mass must lie inside the material
The lines should have met at P
The method only works for objects heavier than 1 kg
3.
The diagram shows a cone at rest on a table. Which type of equilibrium is it in, and why?
Dr Dabour Hub Academy - figure 2
Unstable – a small push lowers the centre of mass, so it topples further
Stable – a small push raises the centre of mass, so it returns
Neutral – a small push keeps the centre of mass at the same height, so it stays in its new position
Not in equilibrium – there is a resultant force on it
4.
The truck in the diagram is parked across a 30° slope. Will it topple over sideways?
Dr Dabour Hub Academy - figure 3
Yes – any slope steeper than 20° tips a truck over
Yes – the centre of mass is above the lower wheel
No – the vertical line through the centre of mass still falls within the base; it would only topple beyond about 40°
No – trucks cannot topple because their weight acts at the wheels
5.
Using the table of equilibrium types, a marble resting at the bottom of a round bowl is nudged slightly. Which type of equilibrium is it in?
Stable – the nudge raises its centre of mass, so it rolls back
Unstable – the nudge lowers its centre of mass
Neutral – its centre of mass stays at the same height
It is not in equilibrium
6.
Why does a person standing on one leg lean their body sideways?
To increase their weight
To reduce their moment of inertia to zero
To make the Coriolis effect cancel
To keep their centre of mass above their small base of support
7.
Designers make vehicles and furniture hard to tip over. Which pairing of design feature and effect on stability is correct?
Narrow wheelbase – wider base, more stable
Luggage on the roof – lowers centre of mass
Tall, narrow lamp – larger toppling angle
Heavy battery low in a bus floor – lowers centre of mass, more stable
8.
As a car turns sharply left, a passenger feels pushed towards the right-hand door. What is the correct explanation?
A real outward centrifugal force pushes them
The passenger's inertia tends to keep them moving in a straight line while the car turns beneath them
The door attracts them magnetically
Their weight acts sideways during the turn
9.
A wheel moves along a straight road at constant velocity while spinning at a constant rate. Is it in equilibrium?
No – it is moving, so it cannot be in equilibrium
No – spinning objects always have a resultant torque
Yes – with no linear or angular acceleration, both ΣF = 0 and Στ = 0
Only in rotational equilibrium
10.
A student raises the centre of mass of a block (base width 0.10 m) by adding weights and measures the tilt angle at which it topples (table). Which result is anomalous?
The result for 0.10 m
The result for 0.20 m
The result for 0.15 m
The result for 0.25 m
11.
A uniform plank 4.0 m long and weighing 400 N rests on two supports, one at its left end and one 1.5 m from its right end. How far beyond the right-hand support can a 750 N person walk before the plank starts to tip?
0.938 m
0.500 m
1.07 m
0.267 m
12.
A metre rule pivoted at its 50 cm mark carries the weights listed in the table. Where must the 2.0 N weight be hung to balance the rule?
At the 80 cm mark
At the 100 cm mark
At the 15 cm mark
At the 85 cm mark
13.
A light rod of length 1.5 m has a 4.0 kg mass at its left end and a 5.0 kg mass at its right end. How far from the left end is the centre of mass?
0.667 m
0.750 m
0.833 m
1.88 m
14.
Three small masses sit on a light metre-stick-like rod: 2.0 kg at x = 0, 2.0 kg at x = 0.4 m and 5.0 kg at x = 1.0 m. Where is the centre of mass?
0.467 m
5.80 m
0.644 m
0.500 m
15.
The uniform ladder in the diagram rests in equilibrium against a smooth (frictionless) wall. What friction force must the ground exert on its foot?
Dr Dabour Hub Academy - figure 4
200 N
75 N
100 N
533 N
16.
A uniform 2.0 m beam weighing 150 N is hinged to a wall at one end and held horizontal by a vertical rope attached to its free end. What is the tension in the rope?
150 N
300 N
37.5 N
75 N
17.
The centre of mass is not always where you might expect. Which pairing of object and position of its centre of mass is correct?
Uniform metre rule – at the 0 cm end
Boomerang – always inside the material
Ring – at its centre, where there is no material
Uniform solid sphere – on its surface
18.
A student tests the stability of blocks by tilting them on a board until they topple. Which is the dependent variable?
The base width of the block
The mass of the board
The tilt angle at which the block topples
The material of the block
19.
Using the table, which of Lamp B, Lamp A, Lamp E, Lamp D can be tilted furthest before it topples?
Lamp A
Lamp E
Lamp B
Lamp D
20.
The uniform metre rule in the diagram balances horizontally on a pivot at the 60 cm mark. Using the principle of moments, what is the weight W?
Dr Dabour Hub Academy - figure 5
0.429 N
5.25 N
1.50 N
1.93 N
21.
Using the method in the table, where is the centre of mass of the card?
At the first hole
At the midpoint of the first line only
At the lowest point of the card
Where the marked lines cross
22.
A block with base width 0.4 m (diagram) is tilted slowly about one bottom edge. Using the dimensions shown, at what tilt angle does it just begin to topple?
Dr Dabour Hub Academy - figure 6
34°
18°
72°
9.5°
23.
The table lists all the vertical forces on a horizontal beam and where they act. Is the beam in equilibrium?
Yes – the upward forces equal the downward forces
No – the upward forces are larger than the downward forces
No – the forces balance, but the clockwise and anticlockwise moments about the left end do not, so the beam will rotate
Yes – any beam at rest is in equilibrium
24.
Why do standing passengers on a moving bus bend their knees and spread their feet?
To lower their centre of mass and widen their base, so they are harder to topple
To increase their weight
To move their centre of mass outside their base
To reduce the Coriolis effect
25.
A weather service logs the rotation of four large storms, all in the Northern Hemisphere (table). Which entry is most likely a recording error?
Storm 1
Storm 2
Storm 3
Storm 4
26.
A hammer is thrown so that it spins as it flies (diagram). Which labelled line does its centre of mass follow?
Dr Dabour Hub Academy - figure 7
B – a wavy path that follows the spinning head
C – a straight line
None – the centre of mass moves randomly
A – a smooth parabola
27.
People in rotating frames notice effects that are not caused by real forces. Which pairing of effect and explanation is correct?
Coriolis effect – a real force exerted by the Sun
Centrifugal force – a real outward force in an inertial frame
Hurricane rotation – caused by ocean tides
Feeling pushed outward on a turning bus – inertia keeps you moving straight
28.
The uniform rod in the diagram hangs horizontally from a single string, with a 6.0 N weight at its left end. How far from the left end must the string be attached?
Dr Dabour Hub Academy - figure 8
0.20 m
0.50 m
0.30 m
0.33 m
29.
A 100 g mass is fixed at the 10 cm mark of a uniform metre rule, and the rule is balanced on a knife edge (table). What is the mass of the rule?
50 g
122 g
82 g
200 g
30.
The first condition for equilibrium is that the resultant _____ on the object is zero.
torque
velocity
force
energy
31.
A cone balanced on its tip is in _____ equilibrium.
stable
neutral
dynamic
unstable
32.
To find the centre of mass of a flat irregular card, it is hung from a pin together with a _____.
plumb line
spring balance
protractor
newton meter
33.
An object that returns to its original position after being slightly displaced is in _____ equilibrium.
stable
unstable
neutral
dynamic
34.
For a uniform beam, its weight can be taken to act at its _____.
left end
midpoint
pivot
heaviest end
35.
In a centre-of-mass investigation, repeating the plumb-line method from a third hole helps check for and reduce errors. True or false?
True
False
False, because extra holes change the centre of mass
True only when the card is square
36.
Racing cars are built with a high centre of mass so they grip the road better when cornering. True or false?
False, because they are built with a low centre of mass and wide base so they resist tipping
True
True only when the track is wet
False, because height has no effect on stability
37.
A ball resting on a flat floor is an example of neutral equilibrium. True or false?
True
False
False, because it is in unstable equilibrium
True only when the floor is tilted
38.
Centrifugal force is a real outward force that acts on passengers in a car going round a corner. True or false?
True
True only when the car is moving fast
False, because it is a real inward force
False, because it is an apparent force in the rotating frame; passengers' inertia tends to keep them moving straight
39.
A light rod of length 2.0 m has a 1 kg mass at one end and a 5 kg mass at the other. Its centre of mass is 1.67 m from the 1 kg mass. True or false?
True
False
False, because it is at the midpoint, 1 m from each mass
True only when the rod is horizontal
40.
Taking moments about the point where an unknown support force acts removes that force from the moment equation. True or false?
False
False, because it doubles the unknown force
True only when the beam is uniform
True
41.
A tilted object will fall back to its original position as long as the vertical line through its centre of mass still passes through its base. True or false?
False
False, because it always topples once tilted
True only when its base is circular
True
42.
An object topples when the vertical line through its centre of mass falls outside its base. True or false?
False
True
False, because it topples only when the base leaves the ground
True only when it is taller than it is wide
43.
For an object in equilibrium, the resultant torque is zero about every point, not just about the pivot. True or false?
False
True
False, because it is zero only about the centre of mass
True only when the object is a uniform beam
44.
The centre of mass of an object must always lie inside the material of the object. True or false?
False, because for objects like rings and boomerangs it lies in empty space
True
True only when the object is uniform
False, because it always lies on the object's surface
45.
An object with zero resultant force on it must be in equilibrium. True or false?
True
True only when it is at rest
False, because the resultant force must be non-zero for equilibrium
False, because equilibrium also requires zero resultant torque; a couple gives zero net force but causes rotation
46.
A beam of weight 300 N carries a 500 N load and is held by two supports pushing up with 400 N and 500 N. The resultant vertical force on it is zero. True or false?
True
False, because the upward forces total 900 N but the downward forces total 800 N
True only when the load is at the centre
False, because the supports must push with equal forces
47.
An object moving at constant velocity with no rotation can be in equilibrium. True or false?
False
True
False, because only objects at rest can be in equilibrium
True only when it is on a frictionless surface
48.
The Coriolis effect causes large-scale winds in the Northern Hemisphere to rotate clockwise around low-pressure regions. True or false?
True
True only when the wind is very weak
False, because in the Northern Hemisphere they rotate counterclockwise
False, because the Coriolis effect only acts at the equator
49.
When a spinning object is thrown, its centre of mass follows a smooth parabolic path. True or false?
False
False, because the centre of mass wobbles with the spin
True only when it is not spinning
True
50.
In a uniform gravitational field the centre of gravity coincides with the centre of mass. True or false?
False
False, because they are always at opposite ends of an object
True
True only when the object is a sphere
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Part of Rotational Motion — see every lesson and quiz in this unit.
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