1. F ˆ F www.schoolDD.com 1
PAT2 ʽ F . 53
1 : 4
ʽ F
F 56 72 ( 17 F ) F 3.0 51
F F
g = 9.8 m/s2
h = 6.6 × 10-34
J s
c = 3.0 × 108
m/s
kB = 1.38 × 10-23
J/K
R = 8.31 J/K.mol
NA = 6.02 × 1023
√૛ = 1.414
√૜ = 1.732
√૞ = 2.236
√ૠ = 2.646
ln 2 = 0.693
e = 1.6 x 10-19
C
G = 6.67 x 10-11
m3
/(kg.s2
)
࣊ = 3.14
F F F
http://www.onetresult.niets.or.th/ExamGATPAT/

2. F ˆ F www.schoolDD.com 2
56.
F . F F ( )
= ½ (6+2)x3 + (-½ x2x1) = 11 m
F . F 0-2 F (3-0)/(2-0) = 1.5 m/s2
F 4-6 F (0-3)/(6-4) = -1.5 m/s2
F
F . F F F
F F
F 1.
57.
F
m1
∑ F = ma
F F = m1a1
F = 8m1 ---(1)
m2
s = ut + ½ at2
F
m1
a1 = 8 m/s2
t = 2 s
s = 48 m
m2 / m1 = ?F
m2 m2
u = 0
a2

3. F ˆ F www.schoolDD.com 3
48 = 0 + ½ a2(2)2
a2 = 24 m/s2
∑ F = ma
F F = m2a2
F = 24m2 ---(2)
(1) = (2) , 8m1 = 24m2
‫׵‬
୫మ
୫భ
=
ଵ
ଷ
F 3.
58.
F F F
F F F 0.5 cos30
F , W = F x 0.5 cos30
W = 40 x 0.5 √ଷ
ଶ
‫׵‬ W = 17.3 J
F 2.
30°
F = 40 N
0.5 m
0.5 cos30

4. F ˆ F www.schoolDD.com 4
59.
F
F
E =
ఙ
ఌ
E =
୊/୅
∆୐/୐బ
F A EA =
୊ఽ/୅ఽ
∆୐ఽ/୐బఽ
---- (1)
F B EB =
୊ా/୅ా
∆୐ా/୐బా
---- (2)
(1) / (2) ,
୉ఽ
୉ా
=
୊ఽ/୅ఽ
∆୐ఽ/୐బఽ
/
୊ా/୅ా
∆୐ా/୐బా
୉ఽ
୉ా
=
୊ఽ/୅ఽ
∆୐ఽ
/
୊ా/୅ా
∆୐ా
(L0A = L0B)
୉ఽ
୉ా
=
୊ఽ
∆୐ఽ୅ఽ
/
୊ా
∆୐ా୅ా
୉ఽ
୉ా
= 2
୅ా
୅ఽ
(
୊ఽ
∆୐ఽ
/
୊ా
∆୐ా
= 2)
୉ఽ
ଶ୉ఽ
= 2
୅ా
୅ఽ
(EB = 2EA)
AA = 4 AB
గ
ସ
dA
2
= 4(
గ
ସ
dB
2
)
dA
2
= 4 dB
2
ΔL
F F
L0 A F
୊ఽ
∆୐ఽ
/
୊ా
∆୐ా
= 2
L0A = L0A
EB = 2EA

5. F ˆ F www.schoolDD.com 5
‫׵‬ dA = 2 dB
F 3.
60.
F F F
2 F F
∑ F = ma
N - W = ma
N = W + ma
F 1 , 2 3 N W F F F a F ˈ + , - 0 F
F 4 F F F F F F
F 3
F 4
N
aW

6. F ˆ F www.schoolDD.com 6
61.
F
F ( ) F 1 F F 0.4
F 0.4 F ߣ = 8 m
v =
ୱ
୲
v =
଼
଴.ସ
‫׵‬ v = 20 m/s
F 2
62.
F F
L/2
W
B
L/4
A
L/3
W
ߣ
( )
12 m
( )
t = 0 s
t = 0.4 s
t = 0.2 s

7. F ˆ F www.schoolDD.com 7
∑ M = W(L/2) = WL/2
∑ M = W(L/6) = WL/6
∑ M > ∑ M F F F 1.
F ∑ M F WL/2 - WL/6 = WL/3 F F
F 4 F F∑ M F (4/3)W(L/4) = WL/3
F 4
63.
F F F
F 1 4 F F 3λ/2
v = fλ
340 = 400 λ
λ = 0.85 m
3λ/2 = 3(0.85)/2
3λ/2 = 3(0.85)/2
3λ/2 = 1.275 m = 127.5 cm
f = 400 Hz
v = 340
m/s
1
λ/4 λ/2
2 3 4

8. F ˆ F www.schoolDD.com 8
F 2
64.
F F F
୊
ୟ
=
୛
୅
୊
஠୰మ
=
୛
஠ୖమ
ୖమ
୰మ
=
୛
୊
ୖమ
୰మ
=
ହ଴଴୶ଽ.଼
ସଽ
ୖమ
୰మ
= 100
‫׵‬
ୖ
୰
= 10
F 2
65.
F F F
F = 49 N
. A
R
W = 500x9.8 N
. a
r
ୖ
୰
= ?
R
r
V
v

9. F ˆ F www.schoolDD.com 9
(Av) F F
F F A1v1 = A2v2
ߨR2
V = ߨr2
v
R2
V = r2
v
F 3
66.
F
F F F
∆Q = ∆U + ∆W
∆Q =
ଷ
ଶ
nR∆T + 0
2493 =
ଷ
ଶ
x5x8.31x∆T
‫׵‬ ∆T = 40 ( F )
F 4
67.
F ˂
ˈ F F F
∆Q = 2493 J
n = 5 mol
∆W = 0
∆T = ?

10. F ˆ F www.schoolDD.com 10
F 1
68.
˂ F 2
F F F
F F F I1
E = I1r + I1R
12 = I1x1 + I1x3
I1 = 3 A
F F I = 2 A ˂ F I2
I = I1 I2
2 = 3 I2
I2 = 1 A
˂ F V2
V2 = I2(R+r)
V2 = 1x4
‫׵‬ V2 = 4 V
F 3
R = 3 Ω
E = 12 V
r = 1 Ω
M

11. F ˆ F www.schoolDD.com 11
69.
˂
F F F F ˂ F C1 , C2 (= C3) ,
C4 F F F F ˂ 12 V F 1 F 3
C2 C3 F F F C1 C4
C2 C3
F C23 = C2 + C3
C23 = 2 + 4
C23 = 6 ߤF
F
ଵ
େ
=
ଵ
େభ
+
ଵ
େమయ
+
ଵ
େర
ଵ
େ
=
ଵ
ସ
+
ଵ
଺
+
ଵ
ଷ
ଵ
େ
=
ଷ
ସ
C =
ସ
ଷ
ߤF
Q C =
୕
୚
Q = C V
Q =
ସ
ଷ
x 12
Q = 16 ߤC
Q = Q1 = (Q2+ Q3) = Q4
F F F F C =
୕
୚
V =
୕
େ

12. F ˆ F www.schoolDD.com 12
V1 =
୕భ
େభ
V1 =
ଵ଺ ఓେ
ସ ఓ୊
V1 = 4 V
V4 =
୕ర
େర
V4 =
ଵ଺ ఓେ
ଷ ఓ୊
V4 = 5.3 V
V2 = V3 = 12 - (V1 + V4)
V2 = V3 = 12 - (4 + 5.3)
V2 = V3 = 2.7 V
F 4
70.
˂ F 1
F ˈ F
ୖభ
ୖయ
=
ୖమ
ୖర
ସ
ଵ଴
=
ଶ
ହ
0.4 = 0.4
‫׵‬ ˈ F F F F 20 Ω
6 V
R3=10 Ω
20 Ω
R2=2 ΩR1= 4 Ω
A
R4= 5 Ω

13. F ˆ F www.schoolDD.com 13
F R1 F R2
F F R12 = R1 + R2
R12 = 4 + 2
R12 = 6 Ω
F R3 F R4
F F R34 = R3 + R4
R34 = 10 + 5
R34 = 15 Ω
F R12 F R34
F F
ଵ
ୖ
=
ଵ
ୖభమ
+
ଵ
ୖయర
ଵ
ୖ
=
ଵ
଺
+
ଵ
ଵହ
ଵ
ୖ
=
଻
ଷ଴
R =
ଷ଴
଻
Ω
˂ I
V = IR
I =
୚
ୖ
I =
଺
యబ
ళ
‫׵‬ I = 1.4 A
F 1
71.
˂ F 2
F
VR ˂ I ( VR = IR)
˂ I F F Z ( I =
୚
୞
)

14. F ˆ F www.schoolDD.com 14
˂ F F F XL (
XL = ߱L = 2ߨfL) F Z F (Z = ඥRଶ ൅ X୐
ଶ
)
F 1
72.
ʽ F F
F ߣ F F F F F
F F 6 F F F 1 F ߣ =
ଵ
଺
F F 2 F ߣ =
ଶ
଺
F F 3 F ߣ =
ଷ
଺
F F n F ߣ =
୬
଺
F F F ߣ F F n ߣ =
୬
଺
F F ߣ n F F ˈ F
ଵ
଺
( F y = mx + c F ߣ ൎ y , n ൎ x , m ൎ
ଵ
଺
c = 0)
F 2

15. F ˆ F www.schoolDD.com 15
2 :
ʽ F
F 98 103 ( 6 F ) F 4.0 24
F F 2 F
: F F F F 5 F ˆ F F
F F 5 F ˆ
F : 1.414 × 2 = 2.828 F ˈ 2.83
1.414 × 3 = 4.242 F ˈ 4.24
9.8 × 5 = 49.0 F ˈ 49.00

16. F ˆ F www.schoolDD.com 16
98.
F F
F
F F + f = mg sin60
F = mg sin60 f
F = mg sin60 ߤ(mg cos60)
F = 5x9.8x√ଷ
ଶ
0.3(5x9.8x
ଵ
ଶ
)
‫׵‬ F = 35.09 N Ans
F
F F = mg sin60 + f
F = mg sin60 + ߤ(mg cos60)
F = 5x9.8x√ଷ
ଶ
+ 0.3(5x9.8x
ଵ
ଶ
)
‫׵‬ F = 49.79 N Ans
F
f
ߤ = 0.3
N
mg cos60 mg
0.1 m
60°
m = 5 kg
mg sin60

17. F ˆ F www.schoolDD.com 17
99.
F
F F F
t = 2
sy = uyt + ½ ayt2
0 = uyt + ½(-g)t2
t =
ଶ୳౯
୥
---(1)
F h
vy
2
= uy
2
+ 2ays
0 = uy
2
+ 2(-g)h
uy = ඥ2gh ---(2)
F uy = ඥ2gh (2) (1)
F t = 2
ඥଶ୥୦
୥
t = ට
଼୦
୥
t2
=
଼୦
୥
22
=
଼୦
ଽ.଼
‫׵‬ h = 4.90 m Ans
u
θ
ux
uy
t = 2 s
h

18. F ˆ F www.schoolDD.com 18
100.
F
F F F
F PV = nRT
V n
F
୔భ
୘భ
=
୔మ
୘మ
ଶସ଴
ଷ଴଴
=
୔మ
ଷଶ଴
‫׵‬ P2 = 256.00 kPa Ans
101.
F
F F F
V1
P1 = 240 kPa
T1 = 273+27 = 300 K
V2 = V1
P2 = ?
T2 = 300+20 = 320 K
ss = 20 cm
C F O
f = 8 cm

19. F ˆ F www.schoolDD.com 19
ଵ
୤
=
ଵ
ୱ
+
ଵ
ୱᇲ
F
ଵ
଼
=
ଵ
ଶ଴
+
ଵ
ୱᇲ
s = 13.33
‫׵‬ s + s = 20 + 13.33 = 33.33 cm Ans
102.
˂
F
A B F ˂ F F F
˂ F 360 F A ˈ 4 F B F A ˈ 4 F
B
F F =
୏୕భ୕మ
୰మ
r F F =
ଽ୶ଵ଴వ୶ଶ଼଼୶ଵ଴షల୶଻ଶ୶ଵ଴షల
ଶమ
‫׵‬ F = 46.66 N Ans ( ˈ
)
r F =
ଽ୶ଵ଴వ୶ଶ଼଼୶ଵ଴షల୶଻ଶ୶ଵ଴షల
ଶ.ଵହమ
‫׵‬ F = 40.37 N Ans
QA = 360 ߤC
aA = 12 cm
QB = 0
aB = 3 cm
QAB = 360 ߤC
F F
QA = 288 ߤC QB = 72 ߤC
r = 200 cm

20. F ˆ F www.schoolDD.com 20
103.
ʽ F
F F F
F ߣ =
୦
୫୴
F mv =
୦
ఒ
v =
୦
୫ఒ
v =
ସ୶ଵ଴షభఱ୶ሺଷ୶ଵ଴ఴሻమ
଴.ହ୶ଵ଴ల୶଴.ସ୶ଵ଴షవ
(c = 3x108
m/s)
v = 1.8x106
m/s
hf = EKmax + W
F hf = ½ mv2
+ W
4x10-15
x4x1015
= ½ x0.5x106
x
ଵ
ሺଷ௫ଵ଴ఴሻమ
x(1.8x106
)2
+ W
‫׵‬ W = 7.00 eV Ans
F F
F F hf
F F F EKmax
F F ˆ F W
hf = EKmax + W
e-
hf
EKmax + W
W = ?
ߣ = 0.4 nm
f = 4x1015
Hz
h = 4x10-15
eVs
me = 0.5 MeV/c2

21. F ˆ F www.schoolDD.com 21
F PAT2 ʽ F ʾ 2552 F
F F F PAT2
ʽ F .
F B2S F