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1. 9
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2. – F ˆ F www.schoolDD.com 1
9
F
F F F
F F F F
F F F F F
9.1 F
F ࣋ F F ˈ F F ˈ
F F (kg/m3
)
- F F F
- F F ˈ F ˈ F F
4˚ C 1.0 x 10 3
kg/m3
F 1
2 F F F 6.0 F F
V =
ସ
ଷ
ߨr3
=
ସ
ଷ
ߨ x 0.033
V = 1.13x10-4
m3
F ρ =
୫
୴
=
ଶ
ଵ.ଵଷ୶ଵ଴షర
‫׵‬ ρ = 1.77 x 104
kg/m3
Ans
ૉ =
‫ܕ‬
‫ܞ‬
d= 0.06

3. – F ˆ F www.schoolDD.com 2
9.2
P F F ( )
ˈ F F ˈ F (Pa)
F
9.2.1 F
Pg ˈ h F
F ߩgh
F P ˈ (Pg) (P0)
1.
2. F
‫۾‬ =
۴
‫ۯ‬
P
P0
Pgh
‫۾‬g = ࣋gh
‫۾‬ = P0 + ࣋gh

4. – F ˆ F www.schoolDD.com 3
3. F F
F F
4. F F F F F
F
5. F ˈ F
F 2
F 5 F
F ˈ F ( F F F 1.02 x 103
kg/m3
) , F 1.0 x105
Pa g = 9.8 m/s2
)
Pg = ߩgh
= 1.02x103
x9.8x5.0
‫׵‬ Pg = 5.0 x 104
Pa Ans
F P = P0 + Pg
= 1.0x105
+ 5.0x104
‫׵‬ Pg = 1.5 x 105
Pa Ans
F 3
F 2 F F F ˈ 2.0 x 105
Pa F
P = P0 + Pg = P0 + ߩgh
h
Pg = ߩgh
h Pg = ߩgh
P = P0 + ߩghP
h
P0
= ߩg
Pg = ߩghPg
h
= ߩg
Pg = ߩghPg
ߩ
= gh
P
Pg
P0 = 1x105
h = 5.0
“ F F F ”

5. – F ˆ F www.schoolDD.com 4
F P = 2x105
F 2x105
= 1.0x105
+ 1.02x103
x9.8xh
‫׵‬ h = 10.0 m Ans
9.3 F
F F = PA
F F
ˈ F
- F F F
F (Po = 0) F F F F
F
F 4
F F F F ʽ F F F 2 F
F F F F (ߩ = 1x103
kg/m3
, g = 9.8 m/s2
)
P0
Pg = ߩgh
h
= A
F P = P0 + Pg
F = PA = (P0 + ߩgh)A
P0Pg top = 0
h= A
Pg bot = ߩgh
P = P0 + ሺ
୔୥ ୲୭୮ ା ୔୥ ୠ୭୲
ଶ
ሻ
F = PA = (P0 +
஡୥୦
ଶ
)A
0
Pg = ߩgh
h = 2
2 x 2
Pg top = 0
Pg bot = ߩgh

6. – F ˆ F www.schoolDD.com 5
F F P = Pg = ߩgh
= 1x103
x9.8x2
P = 1.96x104
Pa
F = PA = 1.96x104
x(2x2)
‫׵‬ F = 7.84x104
N Ans
F P = ሺ
୔୥ ୲୭୮ ା ୔୥ ୠ୭୲
ଶ
ሻ =
஡୥୦
ଶ
=
ଵ୶ଵ଴య୶ଽ.଼୶ଶ
ଶ
P = 9.8x103
Pa
F = PA = 9.8x103
x(2x2)
‫׵‬ F = 3.92x104
N Ans
9.4
1. F
F F F F
2. F
P0
Pgh
PB = PA
P = P0 + Pg
P = P0 + ߩgh
P ( F )
A B
F
P0 Pg h
A B
( ˈ F)
PA = PB
P0 = ߩgh

7. – F ˆ F www.schoolDD.com 6
F 5
F ʽ (P0 =1.0 x 105
Pa , g = 9.8 m/s2
, ߩ =
13.6 x 103
kg/m3
)
PA = PB
P0 + ߩ gh = P
1.0x105
+ 13.6x103
x9.8x0.1 = P
‫׵‬ P = 1.31x105
Pa Ans
F 6
F F F F F
F
F P0 = P + Pg
P = P0 – Pg = P0 - ߩgh
= 1.0x105
- 1.0x103
x9.8x0.05
‫׵‬ P = 9.95x104
Pa Ans
F 7
F F F F
F F
P0
Pgh= 0.1
P = ?
A B
P = ?
P0
h= 0.05 Pg
P0
Pg h= 0.2
A B
P

8. – F ˆ F www.schoolDD.com 7
Pg PA = PB
Pg = ߩ gh
= 13.6x103
x9.8x0.2
‫׵‬ Pg = 2.66x104
Pa Ans
P F PA = PB
P F = Pg + P0
= 2.66x104
+ 1x105
‫׵‬ P F = 1.266x105
Pa Ans
F 8
F F F F F F ˈ 2 F F
F 103
kg/m3
F F 700 kg/m3
10 F F F
F F F
h PA = PB
Pg + P0 = Pg + P0
(ߩgh) = (ߩgh)
700x9.8x0.1 = 103
x9.8xh
‫׵‬ h = 0.07 m
‫׵‬ F F 0.10- 0.07 = 0.03 m Ans
P0
0.1
A B
h= ?
P0

9. – F ˆ F www.schoolDD.com 8
F 9
F x F F ˈ 1x103
kg/m3
PA = PB
PB = PC ˈ F
PC = PD
‫׵‬ PA = PD
P0 + Pg = P0 + Pg x
(ߩgh) = (ߩgh)x
1x103
x9.8x0.1 = ߩx x9.8x0.08
‫׵‬ ߩx = 10/8 x103
= 1.25x103
kg/m3
Ans
9.5
P0
0.1
A B
P0
x
C D
0.08

10. – F ˆ F www.schoolDD.com 9
- F F F
F F
F
- F F F F F F F
F F F F
F
9.6
F F F ʽ F
F F
F 10
F F 10cm2
100 cm2
F
1000 kg F F F F F
F
. a
(P=F/a F
)
F
. A
W
. a
۴
‫܉‬
=
‫܅‬
‫ۯ‬
F = F

11. – F ˆ F www.schoolDD.com 10
୊
ୟ
=
୛
୅
୊
ଵ଴୶ଵ଴షర
=
ଵ଴଴଴୶ଽ.଼
ଵ଴଴଴୶ଵ଴షర
‫׵‬ F = 98 N Ans
F 11
F 10 F ˈ 100 N F F
( ߩ = 800 kg7m3
)
F
F x F
୊
ୟ
=
୛
୅
+ ߩgh
ଵ଴଴
ଵ଴୶ଵ଴షర
=
ଵ଴଴଴୶ଽ.଼
ଵ଴଴଴୶ଵ଴షర
+ 800x9.8xh
‫׵‬ h = 0.25 m Ans
F
. A
W
. a
m = 1000 kg
F = 100 N
. A
W
. a
m = 1000 kg
hx

12. – F ˆ F www.schoolDD.com 11
9.7 F
FB F F F
F F F
- F FB = mg
- F mg > FB
F 12
F F 1 ( ߩ = 1x103
kg/m3
)
. A F 50%
. B F
.
FB = m g = ρ V g
= ρ (0.5V)g
= 1x103
(0.5x1x1x1)x9.8
‫׵‬ FB = 4900 N Ans
mg = FB = 4900 N
m =
୊ా
୥
=
ସଽ଴଴
ଽ.଼
= 500 kg
F ρ =
୫
୚
= 500 kg/m3
mg FB
V
mg FB
V
FB = ૉ V g
FB = m g = ρ V g
FB ↑
mg FB
mg FB
mg FB mg FB
mgFB
FB = mg FB = mg
mg - FB = ma
T + FB = mg
N + FB = mga
T
N
mg FB
V = 0.5V

13. – F ˆ F www.schoolDD.com 12
.
FB = m g = ρ V g
= ρ (V)g
= 1x103
(1x1x1)x9.8
‫׵‬ FB = 9800 N Ans
mg = FB = 9800 N
m =
୊ా
୥
=
ଽ଼଴଴
ଽ.଼
= 1000 kg
F ρ =
୫
୚
= 1000 kg/m3
F 13
˄ ʽ 100 F
5 F ˄ F F F
ˁ ˈ 1.2x103
kg/m3
F ˈ 103
kg/m3
∑ F୷ = 0
FB = F + mg
ρ V g = F + mg
1x103
xVx9.8 = 5 + 0.1x10
V =
଺
ଽ.଼୶ଵ଴య
= 6.12x10-4
m3
ρ =
୫
୚
V =
୫
஡
=
଴.ଵ
ଵ.ଶ୶ଵ଴య
= 0.83x10-4
m3
‫׵‬ ˄ = 6.12x10-4
– 0.83x10-4
= 5.29x10-4
m3
Ans
F 14
F F 60 N F F 50 N F F
( ߩ = 1x103
kg/m3
, g = 10 m/s2
)
mg FB
V =V
mg FB
F=5

14. – F ˆ F www.schoolDD.com 13
T = mg
60 = m(10)
m = 6 kg
T + FB = mg
T + ρ V g = mg
50 + 103
xVx10 = 60
V = 10-3
m3
F ρ =
୫
୚
=
଺
ଵ଴షయ
‫׵‬ ρ = 6x103
kg/m3
Ans
¬ F F F F F F
ˈ F
9.8
F ˈ F F F
F
mg
T
mg FB
T
T l
F
F
F/2
F/2
ʽ F F
L = 2l
T
Fmg
T
L = 2(2ߨr)

15. – F ˆ F www.schoolDD.com 14
઻ ( ) F F F F ˈ
F (N/m)
- L
F
F
-
F 15
F F 5 cm 15 cm 10 F 0.1 (N/m)
F F F F
∑ F୷ = 0
T = F + mg
= γL + mg
= 0.1(0.05+0.15)2 + 0.01x10
‫׵‬ T = 0.104 N Ans
઻ =
۴
‫ۺ‬
T
mg F
L = 2(2ߨr)
l L = 2l
L = 2ߨr

16. – F ˆ F www.schoolDD.com 15
9.8.1 F
- F (cohesive force) ˈ F F
- (adhesive force) ˈ F
- F ˈ F
F F
- F F F F F F
F F F
9.9
F ˈ F
- F
- F F ˈ F F F
F F
F >> F
FB
mg
F
F = 6࣊ࣁrv
ߟ ( ) = (Ns/m2
)
r = (m)
v = (m/s)
v
t
F

17. – F ˆ F www.schoolDD.com 16
-
- F F
F F
F 16
F 2 F
ˈ F F (ρ = 7.8x103
kg/m3
, ρ = 0.8x103
kg/m3
, ߟ = 2.0 Pas, g
= 10 m/s2
)
v ( a = 0)
∑ F = ma = 0
F + FB = mg
F + ρ V g = ρ Vg
F = (ρ - ρ )Vg
= (7.8-.08)x103
x(
ସ
ଷ
ߨ(2x10-3
)3
)x10
‫׵‬ F = 2.34x10-3
N Ans
F = 6ߨߟrv
2.34x10-3
= 6ߨ(2.0)(2x10-3
) v
‫׵‬ v = 6.22x10-2
m/s Ans
9.10 F
(Av) F F
FB
v
mg
F
v1
v2
A1
A2
Av = F
. F
A1v1 = A2v2 F

18. – F ˆ F www.schoolDD.com 17
F 17
F F F F 20 cm F F
0.10 m/s
= Av
=
గ
ସ
(0.2)2
(0.1)
‫׵‬ = 3.14x10-3
m3
/s Ans
F 18
ˈ 100 F F
F F F F 0.1 cm/s F F F
F A1v1 = A2v2
100x0.1x10-2
= 1xv2
‫׵‬ v2 = 0.1 m/s = 10 cm/s Ans
9.10.1 F
F F F F F F F F
F F F
v = 0.1 m/s d = 0.2
v2
A2A1 v1
v1
v2
A2
P + ½ ߩv2
+ ߩgh = F
P1
P2
h1
h2

19. – F ˆ F www.schoolDD.com 18
F h1 = h2
F P1 + ½ ߩv1
2
= P2 + ½ ߩv2
2
F h F F v P F
v F P
F 19
F F F F F F 8 cm2
F 1 F
1 m/s F F 4 cm2
F 9 F F F
3.0 x105
Pa
. F
. F
. v2 = ?
v2 F F A1v1 = A2v2
8x10-4
x1 = 4x10-4
xv2
‫׵‬ v2 = 2 m/s Ans
. P2 = ?
P2 F F P1 + ½ ߩv1
2
+ ߩgh1 = P2 + ½ ߩv2
2
+ ߩgh2
3x105
+ ½ x103
x12
+ 103
x10x1 = P2 + ½ x103
x22
+ 103
x10x9
‫׵‬ P2 = 2.18x105
Pa Ans
P1 + ½ ࣋v1
2
+ ࣋gh1 = P2 + ½ ࣋v2
2
+ ࣋gh2 F
v1 = 1
v2 = ?
A1 = 8x10-4
A2 = 4x10-4
P1 = 3x105
P2 = ?
h1 = 1
h2 = 9

20. – F ˆ F www.schoolDD.com 19
F 20
12 m F 6 m2
2.0 m F
F F F F F
v2 F F P1 + ½ ߩv1
2
+ ߩgh1 = P2 + ½ ߩv2
2
+ ߩgh2
F P1 = P2 = P0 v1 = 0 F ½ ߩv2
2
= ߩg (h1 - h2)
v2
2
= 2 g (h1 - h2)
= 2x10 (12 – 2)
= 200
‫׵‬ v2 = 14.14 m/s Ans
sx F F F sx = uxt = v2t
t sy = uyt + ½ ayt2
2 = 0 + ½ (10)t2
t2
= 0.4
t = 0.63 s
F sx = v2t
= 14.14x0.63
‫׵‬ sx = 8.94 m Ans
h1 = 12
h2 = 2
P1 = P0
v1 = 0
v2 = ? , P2 = P0
sx = ?
A1 = 6
1
2
A2 << A1 F
F F F
v1 = 0

21. – F ˆ F www.schoolDD.com 20
F 21
ʾ F F ʾ 1050 N/ m2
F F ʾ
110 m/s F ʾ F F 1.0 kg/m3
F 1050 N/m2
F F ʾ ʾ
∆P = P2 – P1 = 1050
v2 F F P1 + ½ ߩv1
2
+ ߩgh1 = P2 + ½ ߩv2
2
+ ߩgh2
F ʾ h1 = h2 F ½ ߩ(v1
2
- v2
2
) = (P2 – P1)
½ 1.0(1102
- v2
2
) = 1050
v2
2
= 10000
‫׵‬ v2 = 100 m/s Ans
v1 = 120
v2 = ?
P1
P2