Physics
1.
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
10
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.
1
1
Physics
2.
3.
10
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.
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
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”.
2
1
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.
Physics
5.
10
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.
____
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”.
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.
3
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
:
______________________
2
L
Physics
l
by
re
7.
10
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.)
8.
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".
is
t
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.
Physics
9.
10
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.
FK = 15.d.g.600 ⎫
⎪ FK
⎬⇒ =1
FB
⎪
FB = 30.d.g.300 ⎭
If the container was made upside-down,
the pressure applied by the container on
the horizontal surface would be greater.
5
12.
Two immiscible liquids of densities “2d” and “3d” are
Physics
na
11.
10
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.
t is
nt
,
,
ase
,
n
.
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
3
6
Physics
13.
10
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”.
7
16.
The hydraulic system is in equilibrium as shown in
the figure. Pistons are supposed to be weightless
Physics
14.
10
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.
4
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
s
Physics
16.
of
10
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
4
9
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
Physics
18.
10
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
19.
L
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
"
wn
Physics
20.
10
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
11
/
Physics
21.
10
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.
12
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 = 4hdg3
(The density of water is 1 g/cm .)⎭
Physics
23.
10
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