Unit 4Moments

1. A Bunsen burner is a very stable object because ofitsA high centre ofgravity and broad base

B low centre ofgravity and broad base

C high centre ofgravity and narrow base

D low centre ofgravity and narrow base

2. 'Ihe diagram below shows the first step in an

experiment to determine the position of thecentre of mass of a thin card. What is the nextstep in this experiment?

thin stri

bob

A Measure the thickness of the card.

B Measure the mass of the card.C Hang the card from point R.D Find the midpoint of PQ

3. A metal rod is used to raise a large stone as shownbelow

D

large stoneB rod

small stone

At which position A, B, C, or D should a force be

applied on the rod so that the large stone can be

moved most easily? ( )

4. The diagram shows a balancing toy pivoted on a

stand. Ifthe toy is tilted slightly, it does not topple,but returns to its original position.

weightstand

This is because the centre ofgravity ofthe toy isA inside the weight.B below the pivot.C between the man.D exactly at the pivot. ( )

5. Three blocks X, Y, and Z arebalanced on a beamwith the pivot at the midpoint.

tr FtA

r.r|A

t1fAA

Arrange the blocks in order of increasing mass.

A X,Y,Z B Z,X,Yc x,z,Y D Y,X,Z ( )

card

C

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6. A trap door XY of length 1.00 m and weighing30 N is hinged at the end X. It is opened bypulling a string inclined at an angle 40o to thehorizontal.

30N

Given that the centre of graviq, of the trap dooris 60 cm from X, what is the tension T in thestring required tojust lift the trap door?A 18ON B 6ONc28N D18N ( )

9. A hammer can be suspended in equilibrium fromthree different positions as shown.

CG CGpoint of

.suspensron suspension

point ofCG

of

x

2 3

7.0 10 40 50 100 cm

20N 60NThe diagram shows a uniform metre rule withnegligible weight. What is the force acting at thepivot?

Which of the following matches the figure withtheir gpes of equilibrium?

Neutral Stable UnstableA3 1281,32c273D321()

10. Some passengers are on board a double-deckerbus travelling along a horizontal highway. Thenumber ofpassengers in each deck is as indicated.Which is the most stable bus?

A B

C

11. The diagram below shows a uniform beam XY oflength 1 m supported at P where PX = 20 cm.Thebeam weighs 5 N.

DA 4ONC 8ON

B 2OND 1200N (

8. A heary uniform plank oflength Z is supportedby two forces .E, and F, at points distant L/8 andL/4 from its ends as shown in the diagram below.

U4

L

X P

plank

F1

What is the ratio of Frto F,

F2

: 20cm !;<+i

AC

2:52:3

BD

?

3:53:2

What downward force exerted at X will balance

the beam?

A 5.ON B 7.5Nc 12.5N D 20N ( )

a

a.-

.*ta

a

^<:rta

o

20

.^.30 .^30

^40 .

30

^30 .20

^.40.^

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72. A uniform metre rule is balanced at the 62.0 cm 15

mark with a mass of 24.0 g suspended from the100.0 cm mark as shown in the diagram. What isthe mass of the rule?

62.0 cm

24.0 g

The diagram below shows a ball of diameter30 cm placed against a step of height 15 cm. Ifthe ball has a mass of 15 kg, what minimum forceF applied at a point as shown is required to movethe ball up the step? Assume that the gravitationalforce acting on a mass of 1.0 kg is 10 N.

30 cm

A 1.4.7 gC 38.7 g

B 19.0 gD 76.0 g A 15N

C 15ONB 75ND 3OON

13. The diagram shows a uniform metal bar of length4 m and mass 50 kg. A man pulls straight up witha force F at one end Qof the bar so that it pivotsabout the end P.

When the end Qjust comes offthe ground,what is the value of the force F?

A 25N B 125Nc 25oN D 500N (

74

0.5 m

10N

A bar is hinged to the wall. Three forces act onthe bar. The bar remains in equilibrium. What isthe moment due to the force QA 5Nm B ONmC 10Nm D 20Nm ( )

1,6. A uniform beam PQof length 5 m is placed onend supports and a man ofweight 800 N stands atM such that Q4 = 2 m.The value of the reactionforces at P and Qrespectively, due to the man's

weight are

2m

F

P o

P

A 300 N and 500 NB 320 N and 480 NC 400 N and 400 ND 480 N and 320 N

1.7. An object fixed at one end of a rod is balanced bya 100 g mass as shown. The distance between the100 g mass and the pivot is x.The setup is broughtto the Moon where the gravitational field strengthis 1.6 N/kg.

x

-100 g

object MASS

o

In order to achieve balance,what should the

distance between the 100 g mass and the pivotbe?

Al'6xBxrr 10

c1.6x D* (

15 cm

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5m

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18. Which of the following shows a sphere in stable

equilibrium?o

DC

B

BA

Xo)#

What is the tension 7in the string?A 1.5N B 3.ONC 3.5N D 5.ON

B 5OND 1OON

80gN B 80oN

Jl-u

-

r+r +

1m

R

1000 N

D 900N 6665 900N

+1OOO N (

)

L9. A uniform metre rule is balanced at its centre ofmass as shown in the diagram. When masses Xand Y are hung from positions indicated, the ruleremains in equilibrium.

0 20 50 90 100 cm

What can be concluded about the masses X andY?

A X and Y have the same mass.

B X and Y have the same density.C The ratio of the mass ofX to that ofY is 4:3.

D The ratio of the mass ofX to that of Y is 3:4.()

20. A uniform metre rule of weight 3.5 N is hungfrom a piece of string tied at the 65 cm mark.Themetre rule is balanced by hanging a tnass, nt, at

the end of it.

3.5 N

22. \\e diagram below shows a man of weight800 N standing in the middle of a uniform, rigid,horizontal plank. The plank weighs 1000 N.Which one of the following diagrams shows theforces on the plank?

A 25NC 75N

A

T 900 N 1000 N 900 N

C N

1000 N

27. A square shop sign (of side 1 m) consisting ofa uniform lamina PqRS is attached to a verticalwall by a hinge at P so that S rests against the wallvertically below P. If the mass of the sign is 5 kgthe normal reaction exerted by the wall at S is

23. Abarrel of weight 1500 N and radius 0.5 m rests

against a step of height 0.2 m as shown.

0.2m

What is the smallest horizontal force F through thecentre O needed to push the barrel over the step?A 1125N B 1200Nc 1875N D 2000N ( )

)

F

1mhinge

0.5 m

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OA

oB

OC

D

24. The diagram below shows an oval disc pivotedfreely at point A.Which of the points is the centre of mass of thedisc?

28. Where is the centre of mass of the bus if it doesnot tilt over when travelling at an angle as shownin the diagram below?

25. A child weighing 500 N sits on a see-saw at a

distance of 2 m from the centre of the see-saw.

What force must be exerted at X to balance it?

4m

500 N

29. the centre of a bridge was broken in a storm. Aman of mass 100 kg tried to go over to the otherend, but after 10 m, the bridge started to creakbadly and he had to return. A teenager tried to dothe same and just managed to reach the gap andjumped over.

20m

-

If the gap is 20 m from end A, what is his massin kilogram?

30. A uniform plank oflength 3 m is balanced at itsmidpoint P on a pivot. A 20 N weight is hungfrom the plank at various positions. Which one

of the following moment of force about P is notpossible?

A -10Nm B ONmC 20Nm D 35Nm ( )

A 1OONC 2OON

B 15OND 25ON

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m2

x

26. Auniform metre rule ofweight 0.2 N balances atthe 60 cm mark when a weight W is placed at the80 cm mark. What is the value of W?A 0.1N B 0.15 Nc 0.2N D 0.2667N ( )

27. Which of the following objects, when displaced,is seen to be in neutral equilibrium?A A hear.y weight suspended on a stringB A pencil balanced on its sharp tipC A cone resting on its slant edge

D A pyramid resting on its base ( )

67

250BD

440c50

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31. A uniform metre rule of mass 0.2 kg is supportedby two identical spring balances as shown in thediagram below. The points of suspension are atthe 30 cm and 60 cm mark.

metre rule

cm

End the position at which a 0.1 kg mass mustbe placed such that the spring balances have thesame reading.A 15 cm mark B 25 cm markC 35 cm mark D 45 cm mark

()

32. A uniform metre rule of weight 2.0 N is pivotedat the 60 cm mark. A 4.0 N weight is suspended

at the 100 cm mark, causing the rule to rotateabout the pivot.

0cm 60 cm 100 cm

4.0 N

At the instant when the rule is horizontal, whatis the value of the resultant turning momentabout the pivot?A ZeroB l.4NmclockwiseC l.6NmclockwiseD O.2Nmanticlockwise ( )

33. Which of the diagrams shows how a piece of cardwith centre ofgravity at M hangs when suspendedby a thread?A

34. The apparatus below is set up on Earth. It shows

a piece of soft iron X of mass 0.50 kg 6xed on one

end of a uniform beam AB which is pivoted at itsmidpoint.X is prevented from being pulled downby a fixed magnet by a load of 1.00 kg hung at A.

D

(

cmA B

load1.00 kg

sofl iron X

pivot

magnet

The experiment is now conducted on the Moonwhere the acceleration due to gravity is one-sixththat of the Earth.The mass of the load at A requiredto maintain the equilibrium of the beam is

A 1.00 kg B 3.00 kgC 3.60 kg D 6.00 ks ( )

20N 80N

A 1 metre long bar is held horizontal by two stringswhich have tensions T, and T, Two forces of20 N and 80 N act atthe20 cm and 60 cm marks,respectively. Determine T, and Tr.

T1 T2

60N52N48N40N

35

T2T1

6020

B A 4ONB 48NC 52ND 6ON

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C

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36. The diagram below shows a light rod under the 39action of three vertical forces. The points P, Q, R,S and T are equally spaced out along the rod. Atwhich point must an upward vertical force of 2 Nbe applied to hold the rod in equilibrium?

,1 N

T

1N

2N

BR

37. Below is a lamina of uniform thickness. Its centreof gravlty is most likely to be at

The diagram shows a light rod with two weightshanging from it. A third weight is to be added tobring the system into equilibrium so that the rodis balanced. What weight is required and whereshould it be placed?

0.300 m 0.600 m

S

PDASca_

WerghtA 3.00 NB 3.00 Nc 4.00 ND 4.00 N

Position0.200 m to the left of the pivot

0.200 m to the right of the pivot0.600 m to the right of the pivot0.300 m to the right of the pivot

()

40. Which of the following is in neutralequilibrium?A A heavy weight suspended on a stringB A cone resting on a slant edgeC A heavy based table lampD A pencil balanced on its sharp tip ( )

(

38. The centre of mass of the lamina in the diagramis at B. A disc is then attached as shown. Whichletter shows a possible position of the centre ofmass of the lamina-disc combination?

lamina

disc )

6.00 N 2.00 N

oA

aB

aaCD

.Ar[,oQ

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