Phys102 Final-172 Zero Version Coordinator: Saleem Rao Saturday, May 05, 2018 Page: 1 King Fahd University of Petroleum and Minerals Physics Department c-20-n-30-s-0-e-1-fg-1-fo-0 Q1. A string fixed at both ends has successive resonances with wavelengths of 0.540 m for the nth harmonic and 0.480 m for the (n+1)th harmonic. What is the length of the string? A) 2.16 m B) 1.02 m C) 3.59 m D) 2.94 m E) 4.22 m Ans: = 2 ; +1 = 2 +1 1 +1 − 1 = +1 2 − 2 = 1 2 1 0.48 − 1 0.54 = 1 2 = 2.16 Q2. Two identical sound sources S1 and S2 are placed along a vertical line, as shown in FIGURE 1 and are connected to the same oscillator. When only speaker 1 is ON the intensity of the sound recorded at O is I. If you switch on both speakers what will be the new intensity of the sound at O. A) 4 I B) 2 I C) I D) 8 I E) 3 I Ans: ∝ 2 ⟹ = 2 ′ = (2) 2 ′ = (4 2 ) ′ = 4 Figure 1
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Phys102 Final-172 Zero Version
Coordinator: Saleem Rao Saturday, May 05, 2018 Page: 1
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-30-s-0-e-1-fg-1-fo-0
Q1.
A string fixed at both ends has successive resonances with wavelengths of 0.540 m
for the nth harmonic and 0.480 m for the (n+1)th harmonic. What is the length of the
string?
A) 2.16 m
B) 1.02 m
C) 3.59 m
D) 2.94 m
E) 4.22 m
Ans:
𝜆𝑛 = 2𝐿
𝑛; 𝜆𝑛+1 =
2𝐿
𝑛 + 1
1
𝜆𝑛+1−
1
𝜆𝑛=
𝑛 + 1
2𝐿−
𝑛
2𝐿=
1
2𝐿
1
0.48−
1
0.54=
1
2𝐿
𝐿 = 2.16 𝑚
Q2.
Two identical sound sources S1 and S2 are placed along a vertical line, as shown in
FIGURE 1 and are connected to the same oscillator. When only speaker 1 is ON the
intensity of the sound recorded at O is I. If you switch on both speakers what will be
the new intensity of the sound at O.
A) 4 I
B) 2 I
C) I
D) 8 I
E) 3 I
Ans:
𝐼 ∝ 𝐴2 ⟹ 𝐼 = 𝐾𝐴2
𝐼′ = 𝐾(2𝐴)2
𝐼′ = 𝐾(4𝐴2)
𝐼′ = 4𝐼
Figure 1
Phys102 Final-172 Zero Version
Coordinator: Saleem Rao Saturday, May 05, 2018 Page: 2
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-30-s-0-e-1-fg-1-fo-0
Q3.
An ideal gas that initially occupies a volume of 0.240 m3 at a pressure of 1.01 × 105 Pa
is compressed isothermally to a pressure of 2.20 × 105 Pa. How much energy is
transferred as heat during the compression?
A) −18.9 kJ
B) +18.9 kJ
C) −12.7 kJ
D) +21.2 kJ
E) −16.9 kJ
Ans:
𝑊 = 𝑛𝑅𝑇𝑙𝑛 𝑉𝑓
𝑉𝑖= 𝑃1𝑉1𝑙𝑛
𝑃𝑖
𝑃𝑓
𝑊 = 1.01 × 105 × 0.24 𝑙𝑛 (1.01 × 105
2.2 × 105)
𝑊 = −18871 J
For isotherm Process W = Q
⇒ 𝑄 = −18.9 kJ
Q4.
When 20.9 J was added as heat to a particular ideal gas, the volume of the gas changed
from 50.0 cm3 to 100 cm3 while the pressure remained at 1.00 atm, find CV of the gas.
A) 26.1 J/mol.K
B) 36.2 J/mol.K
C) 12.9 J/mol.K
D) 42.0 J/mol.K
E) 29.7 J/mol.K
Ans:
𝑄 = 𝑛𝐶𝑝 ∆𝑇 = 𝐶𝑝𝑛∆𝑇
𝑄 = 𝐶𝑝 ∙ 𝑃∆𝑉
𝑅
20.9 = 𝐶𝑝 ∙ 1.01 × 105 × 50 × 10−6
8.31
𝐶𝑝 = 34.39
𝐶𝑝 − 𝐶𝑣 = 𝑅
𝐶𝑣 = 34.39 − 8.31 = 26.08
Phys102 Final-172 Zero Version
Coordinator: Saleem Rao Saturday, May 05, 2018 Page: 3
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-30-s-0-e-1-fg-1-fo-0
Q5.
A heat engine absorbs 100 J of heat from the hot reservoir and releases 60 J of heat to
the cold reservoir during each cycle. If each cycle takes 0.50 s, find the power output
of this engine.
A) 80 W
B) 40 W
C) 60 W
D) 20 W
E) 50 W
Ans:
𝑄𝐻 = 𝑄𝐿 + 𝑊
𝑊 = 100 − 60 = 40 J
𝑃 =𝑊
𝑡=
40
0.5= 80 𝑊
Q6.
A particle (charge = +40 μC) is located on the x axis at x = −20 cm, and a second particle
(charge = −50 μC) is placed on the x axis at x = +30 cm. What is the magnitude of the
total electrostatic force on a third particle (charge = −4.0 μC) placed at the origin (x =
0)?
A) 56 N
B) 41 N
C) 16 N
D) 35 N
E) 72 N
Ans:
𝐹𝑇 =𝐾(40 𝜇)(4 𝜇)
(0.2)2+
𝐾(50 𝜇)(4 𝜇)
(0.3)2
𝐹𝑇 = 9 × 109 × 4 × 10−6 [40 × 10−6
(0.2)2+
50 × 10−6
(0.3)2] = 56 N
−4 𝜇𝐶
−50 𝜇𝐶 𝐹1
𝐹2
+40 𝜇
−20
30
Phys102 Final-172 Zero Version
Coordinator: Saleem Rao Saturday, May 05, 2018 Page: 4
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-30-s-0-e-1-fg-1-fo-0
Q7.
A +15.0 nC point charge is placed on the x-axis at x = +1.50 m, and a −20.0 nC
charge is placed on the y-axis at y = −2.00 m. What is the magnitude of the electric
field at the origin?
A) 75.0 N/C
B) 105 N/C
C) 15.0 N/C
D) 45.0 N/C
E) 60.0 N/C
Ans:
𝐸+ =9 × 109 × 15 × 10−9
(1.5)2; 𝐸− =
9 × 109 × 20 × 10−9
22
𝐸+ = 60 𝑁/𝐶; 𝐸− = 45 𝑁/𝐶
𝐸 = √𝐸+2+𝐸−
2 = √602 + 452 = 75.0 𝑁/𝐶
Q8.
A point charge is placed at the center of an imaginary cube that has 20-cm-long edges.
The electric flux out of one of the cube’s sides is –2.5 kN.m2/C. How much charge is
at the center?
A) –1.3 × 10–7 C
B) –2.2 × 10–8 C
C) +1.3 × 10–7 C
D) +2.2 × 10–7 C
E) –6.6 × 10–8 C
Ans:
𝜙𝑡 = 1
𝜀0𝑞𝑒𝑛𝑐
6 × (−2.5 × 103) = 1
𝜀0𝑞𝑒𝑛𝑐
𝑞𝑒𝑛𝑐 = −1.327 × 10−7 𝐶
𝐸+
𝐸− -2 (-20 nC)
(+15 nC)
1.5
Phys102 Final-172 Zero Version
Coordinator: Saleem Rao Saturday, May 05, 2018 Page: 5
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-30-s-0-e-1-fg-1-fo-0
Q9.
The electric potential at points in an xy plane is given by
2 2V 1.2 7.2 4.5 18 Vx x y y . Find the coordinates of the point where the
electric field is zero.
A) (3.0, 2.0)
B) (0, 0)
C) (1.2, 4.5)
D) (7.2, 2.0)
E) (3.0, 7.0)
Ans:
𝐸𝑥 = −𝜕𝑣
𝜕𝑥= −[1.2(2𝑥) − 7.2]
0 = −2.4 𝑥 + 7.2 ⟹ 𝑥 = 3
𝐸𝑦 = −𝜕𝑣
𝜕𝑦= −[−4.5(2𝑦) + 18]
0 = 9𝑦 − 18 ⟹ 𝑦 = 2
Q10.
Rank the potential energies of the four systems of particles shown in FIGURE 2,
GREATEST POSITIVE FIRST.
A) a, (b and d tie), c
B) a, d, c, b
C) (a and d tie), b, c
D) a, (b and c tie), d
E) c, a, b, d
Ans:
A
Figure 2
Phys102 Final-172 Zero Version
Coordinator: Saleem Rao Saturday, May 05, 2018 Page: 6
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-30-s-0-e-1-fg-1-fo-0
Q11.
Five identical capacitors of capacitance C0 = 6.0 μF are connected in a so-called bridge
network, as shown in FIGURE 3. What is the equivalent capacitance between points a
and b?
A) 12 μF
B) 30 μF
C) 15 μF
D) 10 μF
E) 21 μF
Ans:
1
𝐶𝑡𝑜𝑝=
1
𝐶0+
1
𝐶0=
2
𝐶0
𝐶𝑡𝑜𝑝 = 𝐶𝑏𝑜𝑡 = 𝐶0
2
𝐶𝑡𝑜𝑡 = 𝐶0
2+
𝐶0
2+ 𝐶0 = 2𝐶0 = 2 × 6 = 12 𝜇𝐹
Q12.
A cylindrical resistor of radius 5.0 mm and length 2.0 cm is made of a material that
has a resistivity of 3.5 × 10–5 Ω-m. What is the potential difference across the resistor
when the energy dissipation in the resistor is 3.0 W?
A) 0.16 V
B) 0.035 V
C) 1.2 V
D) 0.29 V
E) 0.092 V
Ans:
𝑃 =𝑉2
𝑅=
𝑉2
𝜌 𝑙𝐴
= 𝑉2𝐴
𝜌𝑙
3 =𝑉2(𝜋(5 × 10−3)2)
3.5 × 10−5 × 0.02⟹ 𝑉 = √
3 × 7 × 10−7
𝜋 × (5 × 10−3)2= 0.163 𝑉
Figure 3 Figure 3
Phys102 Final-172 Zero Version
Coordinator: Saleem Rao Saturday, May 05, 2018 Page: 7
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-30-s-0-e-1-fg-1-fo-0
Q13.
Three ideal batteries are connected in the circuit shown in FIGURE 4. If the potential
of point A is 10 V, find the potential of point B.
A) 12 V
B) 22 V
C) 2.0 V
D) 14 V
E) 20 V
Ans:
Current in the loop
𝐼 =34
17= 2𝐴
𝑉𝐴 + 12 − 20 + 10 = 𝑉𝐵
10 + 22 − 20 = 𝑉𝐵
12 𝑉 = 𝑉𝐵
Q14.
FIGURE 5 shows three circuits where all batteries, resistors and capacitors are
identical. Rank the circuits according to the charging time constant (RC) of the
circuits. GREATEST FIRST.
A) 1, 3, 2
B) 1, 2, 3
C) 3, 2, 1
D) 2, 1, 3
E) 1, (2 and 3 tie)
Ans:
𝐴
Figure 4
Figure 5
Phys102 Final-172 Zero Version
Coordinator: Saleem Rao Saturday, May 05, 2018 Page: 8
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-30-s-0-e-1-fg-1-fo-0
Q15.
Two ideal batteries are connected across a set of resistors shown in FIGURE 6. If the
current i = 0.50 A, at what rate is the battery of emf 15 V providing energy to the
circuit shown?
A) 7.5 W
B) 12 W
C) 15 W
D) 5.8 W
E) 1.7 W
Ans:
𝑉𝐴𝐵 = 20 × 0.5 = 10 𝑉
𝑉𝐴 − 10𝐼 − 15 = 𝑉𝐵
𝑉𝐴 − 𝑉𝐵 = 15 + 10 𝐼
10 − 15 = 10 𝐼
−5
10= 𝐼
𝐼 = −0.5 𝐴
𝑃 = 𝜀𝐼 = 15(0.5) = 7.5 𝑊
Q16.
An ideal battery of emf ξ is connected in the circuit as shown in FIGURE 7. If the
current through 10 Ω resistor 1.0 A, find the emf ξ of the battery.
A) 26 V
B) 10 V
C) 20 V
D) 16 V
E) 38 V
Ans:
𝐼1 = 𝑉
𝑅=
10
60=
1
6 𝐴
𝐼2 = 𝐼𝑡 = 3 +1
6=
19
6 𝐴
𝜀 = 10 +19
6 (5) = 10 +
95.0
6= 25.83 𝑉
Figure 6
A
B
Figure 7
𝐼2
𝐼1
3 𝐴
2 𝐴
Phys102 Final-172 Zero Version
Coordinator: Saleem Rao Saturday, May 05, 2018 Page: 9
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-30-s-0-e-1-fg-1-fo-0
Q17.
In FIGURE 8 all the batteries are ideal. Find the current through 6.0Ω resistor.
A) 0.91 A
B) 0.73 A
C) 0.50 A
D) 1.3 A
E) 0.65 A
Ans:
4 − 2𝐼 − 6(𝐼 + 1.64) = 0
4 − 2𝐼 − 6𝐼 − 9.84 = 0
−8𝐼 = 5.84
𝐼 = −0.73 𝐴
∴ 𝐼6−Ω = −0.73 + 1.64 = 0.91 𝐴
Q18.
An electron has a velocity of 6.0 × 106 m/s in the positive x direction at a point where
the magnetic field has the components By = 1.5 T, and Bz = 2.0 T. What is the
magnitude of the acceleration of the electron at this point?
A) 2.6 × 1018 m/s2
B) 2.1 × 1018 m/s2
C) 1.6 × 1018 m/s2
D) 3.2 × 1018 m/s2
E) 3.7 × 1018 m/s2
Ans:
𝐹 = 𝑒 (�̅� × �̅�)
= 1.6 × 10−19 [6 × 106 𝑖̂ (1.5 𝑗̂ + 2 �̂�)]
𝐹 = 9.6 × 10−13[1.5 �̂� − 2𝑗̂]
�⃑� =�⃑�
𝑚=
9.6 × 10−13
9.11 × 10−31(1.5 �̂� − 2𝑗̂)
�⃑� = 1.0537 × 1018(1.5 �̂� − 2𝑗̂)
|�⃑�| = 2.634 × 1018 𝑚/𝑠2
I
I+1.64
Figure 8
Phys102 Final-172 Zero Version
Coordinator: Saleem Rao Saturday, May 05, 2018 Page: 10
King Fahd University of Petroleum and Minerals
Physics Department c-20-n-30-s-0-e-1-fg-1-fo-0
Q19.
A proton travels through uniform magnetic and electric fields. The magnetic field is
ˆ2.5 .B i mT At one instant the velocity of the proton is ˆ2000 /v j m s At that
instant (in unit vector notation), what is the net force acting on the proton if the