Pressure Worksheet - Answer Key-1.pdf

Physics

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Three identical cubes are arranged as in three different (I, II and II) positions on a horizontal surface. The pressure applied on the horizontal surface by the cubes in arrangement I is “P”. 2. Solid objects K and L are placed on a horizontal surface in two different arrangements as shown in Figure-1 and Figure-2.

PRESSURE Solid & Liquid Pressures

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Pressure & Buoyancy Worksheet : Solid & Liquid Pressure

1. Solid objects X, Y and Z are made of the same substance. The pressures applied by X, Y, Z on the horizontal surface are PX, PY, PZ and the magnitudes of the forces applied by them on the horizontal surface are FX, FY, FZ. (“A” represents the base areas of the objects.)

2.

What are the pressures applied on the horizontal surface by the cubes in arrangement II and III in terms of “P”?





Read the following statements. If the statement is ABSOLUTELY CORRECT print "A", if it is POSSIBLE print "P" or if it is WRONG then print "W". You have to correct the wrong statements by using an appropriate word(s) of phrase(s).

a) Compare PX, PY and PZ.

PZ > PY > PX b) Compare FX, FY and FZ.

P ____

FZ > FY > FX

The weight of object K is equal to the weight of object L.

A ____

2. Solid objects K and L are placed on a horizontal surface in two different arrangements as shown in Figure-1 and Figure-2.

The pressure applied by the objects in 4. Figure-2 is greater than the pressure Two cylinders X andapplied Y are placed a horizontal by the on objects in Figure-1. surface as shown in the figure. The radius of cylinder Y is twice the radiusThe of cylinder X and their by heights A ____ total force applied the objects on are equal. The pressure applied by cylinder X on the is the horizontal surface in Figure-1 horizontal surface is “P” and the pressure applied by equal to the total force applied by the cylinder Y on the horizontal surface is “2P”. objects on the horizontal surface in Figure-2.

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Pressure & Buoyancy Worksheet : Solid & Liquid Pressure

Solid objects K and L are placed on a horizontal 3. surface in two different arrangements as shown in Three identical cubes are arranged as in three Figure-1 and Figure-2. different (I, II and II) positions on a horizontal surface. The pressure applied on the horizontal surface by the cubes in arrangement I is “P”.

4.

4. Two cylinders X and Y are placed on a horizontal surface as shown in the figure. The radius of cylinder Y is twice the radius of cylinder X and their heights are equal. The pressure applied by cylinder X on the horizontal surface is “P” and the pressure applied by cylinder Y on the horizontal surface is “2P”.



What are the pressures applied on the horizontal surface the cubes instatements. arrangement II and III in Readby the following If the statement is terms of “P”? ABSOLUTELY CORRECT print "A", if it is POSSIBLE print "P" or if it is WRONG then print "W". You have to 3G correct the wrong statements by P = using an appropriate word(s) of phrase(s).

What would the pressure be, in terms “P”, on the horizontal surface if cylinder X is placed on the top of cylinder Y?

A

____

The weight of object K is equal to the weight 3Gof object G L. P

PII = ____

____

3A

=

A

⇒ PII =

3

The pressure applied by the objects in Figure-2 is greater than the pressure applied by the objects in Figure-1.

3G P PIII = ⇒ PIII = The 2A total force applied 2 by the objects on

the horizontal surface in Figure-1 is equal to the total force applied by the objects on the horizontal surface in Figure-2. 4. Two cylinders X and Y are placed on a horizontal surface as shown in the figure. The radius of cylinder

2

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GX P = 2 ⇒ GX = Pπ r 2 πr GY 2 2P = ⇒ G = 8P π r Y 2 4π r GX + GY (Pπ r 2 ) + (8Pπ r 2 ) Pfinal = = 2 4π r 4π r 2 9P Pfinal = 4

containers are related as mL>mK>mM.

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Pressure & Buoyancy Worksheet : Solid & Liquid Pressure 6. 7. A liquid is poured into a container that some is placed on a Containers X and Y are identical. X contains surface shown in the on figure. liquid ashorizontal in the figure. Theas liquid pressure the The bythe theforce liquidapplied on the by base base ofpressure containerapplied X is “P”, theof the the force applied bythe theforce liquid on the liquid oncontainer the baseisof“P”, container X is “F” and the container is “F” and thesurface force applied by applied base by theofcontainer on the horizontal is “Fh”. the container on the horizontal surface is “Fh”. (Figure is composed of identical squares.)

5. Three containers K, L, M are placed on a horizontal surface as shown in the figure. The forces applied by the liquids on the bases of containers K, L and M are equal.

6.

Read the following statements. If the statement is ABSOLUTELY CORRECT print "A", if it is POSSIBLE print "P" or if it is WRONG then print "W". You have to correct the wrong statements by using an appropriate word(s) of phrase(s).

P ____ P ____ P ____ P ____ A ____

How would “P”, “F” and “Fh” change if the container were placed onIfits having Read the following statements. thesurface statement is base areaprint of “A”? CORRECT "C" or if it is WRONG then print

The liquid pressures at the bottom of the containers are equal.

"W". You have to correct the wrong statements by increases P appropriate : ______________________ using an word(s) of phrase(s).

The base areas of the containers are equal.

____

The densities of the liquids in the containers are related as dL>dK>dM.

____

The heights of the liquids in the containers are related as hM>hK>hL. The masses of the liquids in the containers are related as mL>mK>mM.

____

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decreases F If the :liquid in______________________ container X was poured into container Y, the liquid pressure on the base of container Y would “P/2”. remains thebesame Fh : ______________________

If the liquid in container X were poured into container Y, the force applied by the liquid on the base of container Y would be “F/2”. If the liquid in container X were poured into container Y, the force applied by container Y would be “Fh”.

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L

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K

M

into container Y, the force applied by container Y would be “Fh”.

Pressure & Buoyancy Worksheet : Solid & Liquid Pressure

6. 7. A liquid is poured into a container that is placed on a Containers and Y are contains horizontalX surface as identical. shown inXthe figure. some The liquid as in the figure.by The on the pressure applied theliquid liquidpressure on the base of the base of container X the is “P”, theapplied force applied the on the container is “P”, force by theby liquid liquid on of thethe base of container is “F” theapplied force by base container is “F”Xand theand force applied by the container on the horizontal the container on the horizontal surfacesurface is “Fh”.is “Fh”. (Figure is composed of identical squares.)

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8. A container is fulfilled with a liquid as shown in the figure. The areas of the lateral surfaces X and Y are "3A" and "A" respectively. The force applied by the liquid on lateral surface X is "F".

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e

How would “P”, “F” and “Fh” change if the container were placed on its surface having base Read the following statements. If the statement is area of “A”? CORRECT print "C" or if it is WRONG then print "W". You have to correct the wrong statements by P : ______________________ using an appropriate word(s) of phrase(s).

CF ____ Fh W ____



C ____

What is the force applied by the liquid on the lateral surface Y in terms of "F"?

3h 9hdgA FX = F = .d.g.3A = 2 2

______________________ If :the liquid in container X was poured into container Y, the liquid pressure on the base of container Y would be “P/2”. : ______________________ If the liquid in container X were poured into container Y, the force applied by the liquid on the base of container Y would be “F/2”. 3F/2 If the liquid in container X were poured into container Y, the force applied by container Y would be “Fh”.

2

5h 5hdgA FY = .d.g.A = 2 2 5F FY = 9

4

the horizontal surface would be greater.

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Pressure & Buoyancy Worksheet : Solid & Liquid Pressure 10. 11. The dimensions ofwith a rectangular Two containers are filled two liquidscontainer X and Y are as 15 cm, 20 The cm and 30 of cm. It is X completely filled a liquid. in figure. weight liquid is “G1” and the with weight by the liquidbyonliquid the lateral surface of liquidThe Y isforce “G2”.applied The force applied X on the is container "FK" and the force applied by the liquid on the base ofKits is “F 1” and the force applied by of the container is "FB". is “F2”. The ratio liquid Ybase on the base of its container of F1 to F2 is 1/2.

9. Two immiscible liquids X and Y are in equilibrium in a closed container as shown in the figure.

10.

Read the following statements. If the statement is CORRECT print "C" or if it is WRONG then print "W". You have to correct the wrong statements by using an appropriate word(s) of phrase(s).

W ____

What is the ratio G1 to What is theofratio ofGF2K?to FB?

If the container was made upside-down, the liquid pressure at the bottom of the container would not change.

AB = 15.20 = 300 cm2

increase

C ____

C ____

10.

AK = 20.30 = 600 cm2

If the container was made upside-down, the force applied by the liquids at the base of the container would be less.

If the container was made upside-down, the pressure applied by the container on the horizontal surface would be greater.

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FK = 15.d.g.600 ⎫ ⎪ FK ⎬⇒ =1 FB ⎪ FB = 30.d.g.300 ⎭

12. Two immiscible liquids of densities “2d” and “3d” are

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the pressure applied by the container on the horizontal surface would be greater.

Pressure & Buoyancy Worksheet : Solid & Liquid Pressure

11. Two10. containers are filled with two liquids X and Y as The dimensions of liquid a rectangular are 15 cm, in figure. The weight of X is “G1” container and the weight 20 cm cm.force It is completely filled with liquid. of liquid Y isand “G230 ”. The applied by liquid X onathe force applied liquid on theapplied lateralby surface baseThe of its container is by “F1the ” and the force "FKthe " and theofforce applied by the on the liquidK Yison base its container is “F The ratio 2”. liquid of F1base to F2of is the 1/2.container is "FB".

12. Two immiscible liquids of densities “2d” and “3d” are poured into a container as shown in the figure. The surface areas of lateral surfaces are “A” and “2A”. The force exerted by the liquid on the lateral surface having area of “A” is “F”.

What is the ratio of G1 to G2?

Calculate the forces exerted by the liquid on the lateral surface having the area of “2A” and on the base of the container in terms of “F”?

12.

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cm,

What is the ratio of FK to FB?

VY = 3V ⇒ VX = 7V A A = A ⇒ Ay = A

AB = 15.20 = 300 cm2 AK = 20.30 = 600 cm2

F1 1 h.dX .g.A ⎫ dX 1 = = = ⎬⇒ F2 2 h.dY .g.A ⎭ dY 2

FK = 15.d.g.600 ⎫ ⎪ FK ⎬⇒ =1 FB ⎪ FB = 30.d.g.300 ⎭

G1 dX .VX .g 1.7V 7 = = = G2 dY .VY .g 2.3V 6

12. Two immiscible liquids of densities “2d” and “3d” are poured into a container as shown in the figure. The

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Pressure & Buoyancy Worksheet : Solid & Liquid Pressure

13. Four containers X, Y, Z and T are placed on a horizontal surface. Containers X, Y and Z are filled with liquids and container T is empty. The liquid pressures at the bottoms of the containers X, Y and Z are all equal to "P". (The liquids in the container are immiscible.)

15. Two miscible liquids having densities of “d” and “2d” are as d in the P in= equilibrium 4hdXg ⇒ =figure. 3d ⎫ The liquid pressure X at point X is “P”. ⎪ (“A” and “2A” represent the cross-sectional areas of ⎪ the columns of the combined container.)

⎪ P = 2hdY g ⇒ dY = 6d⎬ ⇒ P = 12hdg ⎪ ⎪ P = 3hdzg ⇒ dZ = 4d ⎪⎭

⎛ 5h ⎞ PT =will + ⎜ pressure .4d.gat⎟ point + ( 3hdg (6hdg What be the )liquid X in ) ⎝ valve ⎠ and the 4 is opened terms of “P” after the

If the liquids were poured into container T, what would be the total liquid pressure at the bottom of container T in terms of "P"?

final equilibrium had reached?

PT = 14hdg

T h h h h

3d 4d 6d

7P PT = 6

h 5h/4 h

14. The hydraulic system is in equilibrium as shown in the figure. The piston is supposed to be weightless and frictionless. The pressure at point X is “P”.

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16. The hydraulic system is in equilibrium as shown in the figure. Pistons are supposed to be weightless

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Pressure & Buoyancy Worksheet : Solid & Liquid Pressure

14. 13. The hydraulic systemX,isY, in Zequilibrium shown Four containers and T are as placed on in a the figure. The surface. piston isContainers supposed to weightless horizontal X, be Y and Z are filled and frictionless. The container pressure T atispoint X isThe “P”.liquid with liquids and empty. (“A” and “2A” represent the cross-sectional areas ofand Z pressures at the bottoms of the containers X, Y are all equal "P". the columns of thetocombined container.) (The liquids in the container are immiscible.)

15. 16. Two miscible liquids having densities of “d” and “2d” in equilibrium figure. The Theare hydraulic systemas is in in the equilibrium as liquid shownpressure in pointPistons X is “P”.are supposed to be weightless the at figure. and “2A”Arepresent the cross-sectional areas of and(“A” frictionless. 1 and A2 are the base areas of the the columns of theofcombined container.) pistons. The density liquid is “d”.

If the liquids were poured into container T, what liquid pressure the bottom Whatwould wouldbebethe thetotal pressure at point Xat(in terms in terms of "P"? of P),ofifcontainer the pistonT were pushed from level K to level L?

What be the statements. liquid pressure at point X in is Read thewill following If the statement terms ofprint “P” after the is opened and the CORRECT "C" or if valve it is WRONG then print final equilibrium had reached? "W". You have to correct the wrong statements by using an appropriate word(s) of phrase(s). /

15.

Vinitial = Vfinal ⇒ 4Ah + 2Ah = h .3A

/ h ____ = 2h The liquid pressure at point X is equal to

“h.d.g”.

(d.4V) + (2d.2V) 4d dmix = = 4V + 2V 3 ____ The liquid pressures at point X and Y are



P PXinitial = P = 2hdg ⇒ hdg = 2 14. 5hsystem is in equilibrium 5Pas shown in The hydraulic PXfigure. =The piston dg ⇒ PX final = to be weightless the is supposed final 2 The pressure at point 4 X is “P”. 8 and frictionless.

equal.

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P = 2hdg ⎫ ⎪ at/point4P ____ The total pressure X is greater ⇒ P =at point Y. 4d ⎬ than the liquid pressure / 16. 3 P = 2h. .g⎪ The hydraulic 3 system ⎭ is in equilibrium as shown in the figure. Pistons are supposed to be weightless

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Pressure & Buoyancy Worksheet : Solid & Liquid Pressure

16. The hydraulic system is in equilibrium as shown in the figure. Pistons are supposed to be weightless and frictionless. A1 and A2 are the base areas of the pistons. The density of liquid is “d”.

17.

Read the following statements. If the statement is CORRECT print "C" or if it is WRONG then print "W". You have to correct the wrong statements by using an appropriate word(s) of phrase(s).

s

C ____ C ____ C ____

17. The flow rates of the valves M and N are the same. They are open at the same time and the final equilibrium is reached. The liquid pressures at the points X, Y and Z are PX, PY and PZ. (All the columns of the combined container have the same cross-sectional area. Dotted lines are equally spaced.)

How can PX, PY and PZ be compared?

After the valves are opened

The liquid pressure at point X is equal to “h.d.g”.

M N

The liquid pressures at point X and Y are equal. The total pressure at point X is greater than the liquid pressure at point Y.

X

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Y

Z 18. Liquid A of density liquid PX"2d" = Pand PZ B of density "3d" Y < are in equilibrium in a combined container as shown

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Pressure & Buoyancy Worksheet : Solid & Liquid Pressure

18. 17. TheAflow rates of theand valves M and are the"3d" same. Liquid of density "2d" liquid B of N density are openinatathe same time and theasfinal are They in equilibrium combined container shown equilibrium is reached. The liquid pressures at the in the figure. points X, Ypressure and Z are X, PY and PZ. (Atmospheric is P ignored.) (All the columns of the combined container have the same cross-sectional area. Dotted lines are equally spaced.)

K

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What is the pressure at point X in terms of "hdg"? How can PX, PY and PZ be compared?

PK = PL = 4hdg + 9hdg = 13hdg 7h PL = 13hdg = .3d.g +PX 2 5hdg PX = 2



20.19. A combined container container is in equilibrium Column K of a combined is filledwhen with an a object of mass is placed onliquid piston K and object liquid as shown in "m" the figure. The pressure on theof bottom column K is “P” when the is in the mass of "2m" is placed on piston L asvalve shown figure. K and L are weightless and frictionless closed. Their cross-sectional areas are "A" andof"3A" (“A”pistons. and “2A” represent the cross-sectional areas TheL vertical distance between the levels therespectively. columns K and of the combined container.) of the pistons is "h".

18. Liquid A of density "2d" and liquid B of density "3d" are in equilibrium in a combined container as shown 10 5 in the figure.

If the places of the objects were interchanged, would be theand vertical distance between Thewhat valve is opened the final equilibrium is the levels What of thewill pistons in liquid terms pressure of "h"? in terms reached. be the

of “P” at the bottom of column K?

1st condition; mg 2mg m = + hdg ⇒ = 3hd A 3A A 2nd condition; 2mg mg / 5m / = + h dg ⇒ = h d 20. A 3A 3A Column K of a combined container is filled with a / liquidhas =shown 5h in the figure. The liquid pressure on the bottom of column K is “P” when the valve is

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Pressure & Buoyancy Worksheet : Solid & Liquid Pressure

20. Column K of a combined container is filled with a liquid as shown in the figure. The liquid pressure on the bottom of column K is “P” when the valve is closed. (“A” and “2A” represent the cross-sectional areas of the columns K and L of the combined container.)

Vinitial = Vfinal ⇒

6Ah = ( 2A + 3A ) .h/ h/ = 2h A

5h

The valve is opened and the final equilibrium is reached. What will be the liquid pressure in terms of “P” at the bottom of column K?

2h

The valve is closed; P P = 6hdg ⇒ hdg = 6

2h

h K

L

horizontal

The valve is opened; P P = 2hdg ⇒ P = 3 /

5

2A

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Pressure & Buoyancy Worksheet : Solid & Liquid Pressure

21. Two immiscible liquids X and Y are poured into a container and their equilibrium condition is given in the figure. The density of liquid X is “3d” and the density of liquid Y is “2d”. The liquid pressure at point L is two times the liquid pressure at point K.

22.

22. 23. Liquid X having density of “d” “d” andand weight of X “G” is in The liquids of densities “2d”, liquid are poured into in the shown thefigure. figure. The equilibrium a container U-tube asas shown ininthe liquid pressure at the bottom of the container is “P”. The empty part of the container is filled with liquid Y having weight of “2G”. (Container is composed of identical cubic parts.)

What is the density of liquid X in terms of “d”? If liquids X and Y are miscible, what will be the liquid pressure at the bottom of the container in terms of “P”?

What is the ratio of h1 to h2?

VX = 2V ⇒ VY = V G = d.2V.g ⎫ ⎬ ⇒ dY = 4d 2G = dY .V.g⎭

⎫ ⎪ PK 1 = ⎬⇒ PL 2 ⎪ PL = (h1.2d.g) + (h2 .3d.g) ⎭ PK = h1.2d.g

(d.2V) + (4d.V) dmix = = 2d V + 2V 24.

h1 3 4h1 = 2h1 + 3h2 ⇒ = h2 2 22.

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Mercury is poured into a U-tube as given in Figure-1. The left arm of the U-tube has a cross-sectional area 2 of 10 cm , and the right arm has a cross-sectional P = hdg ⎫ of water 2 / area of 5 cm . One hundred grams⇒ are then P = 4P ⎬ / into the right arm, as shown in Figure-2. poured P = 2h.2d.g = 4hdg 3 (The density of water is 1 g/cm .)⎭

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Pressure & Buoyancy Worksheet : Solid & Liquid Pressure

23. The liquids of densities “2d”, “d” and liquid X are in equilibrium in a U-tube as shown in the figure.

22. Liquid X having density of “d” and weight of “G” is poured into the container as shown in the figure. The liquid pressure at the bottom of the container is “P”. The empty part of the container is filled with liquid Y having weight of “2G”. (Container is composed of identical cubicofparts.) What is the density of liquid X in terms “d”?

24.

24. Mercury is poured into a U-tube as given in Figure-1. The left arm of the U-tube has a cross-sectional area 2 of 10 cm , and the right arm has a cross-sectional 2 area of 5 cm . One hundred grams of water are then poured into the right arm, as shown in Figure-2. 3 (The density of water is 1 g/cm .)

=x 2x A

2x B

a) What is the length of the water column in the right arm of the U-tube in cm? If liquids X and Y are miscible, what will be the liquid pressure at the bottom of the container in terms of “P”?

PA = PB

24. Mercury is poured+into a U-tube given in Figure-1. (3h.d.g) (h.d .g) =as4h.2d.g X The left arm of the U-tube has a cross-sectional area 2 of 10 cm , and (3d) the right arm )has a cross-sectional + (d 2 X = 8d area of 5 cm . One hundred grams of water are then poured into the right d arm,=as shown in Figure-2. 5d X 3 (The density of water is 1 g/cm .) 13

Vwater = 100 cm3 100 hwater = = 20 cm 5 3

b) If the density of mercury is 13,6 g/cm , what distance (h) will the mercury rise in the left arm?

PA = PB 3x.1.g = 20.13,6.g ⇒ x = 0,49 cm