167. One mole of a monatomic ideal gas undergoes an isobaric process during which $J\,40$ of work is done on the surroundings. What is the change in internal energy of the gas in joules?

• [(1)] $150$
• [(2)] $100$
• [(3)] $60$
• [(4)] $20$

168. An ideal gas undergoes two processes from state a to state c via state b. If the work done along this path on the gas is W, and the heat given to the gas is Q, and $\Delta U$ is the change in internal energy of the gas, what are the signs of Q, W, and $\Delta U$ respectively?
[Figure: P-V diagram showing a process from point a to point b (horizontal, increasing V) then from b to c (curved, increasing P and decreasing V), labeled ``irreversible'']

• [(1)] positive, zero, and positive
• [(2)] positive, positive, and positive
• [(3)] positive, negative, and zero
• [(4)] negative, positive, and positive

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169. Electric charges $+q$, $q_1 = +q$ and $q_2 = q_3 = +3q$ are placed at the vertices of an equilateral triangle, and the electric charge $q_4 = -q$ is placed at the centroid of this triangle, kept fixed. If the force exerted by $q_1$ on $q_4$ is $0.5$ newtons, what is the resultant of the forces exerted on $q_4$ in newtons?
(1) zero (2) $0.5$ (3) $1$ (4) $0.5\sqrt{3}$

170. Two charged particles are placed at two vertices of a triangle as shown in the figure below. The net electric field of these two charges at the other vertex is according to the figure. $\dfrac{q_1}{q_2}$ is equal to which of the following?
[Figure: Right triangle with legs 5 cm and 12 cm, hypotenuse 13 cm; charges $q_1$ and $q_2$ at the base vertices, point E at the top; electric field direction shown]
$$\frac{25}{144} \ (1) \hfill \frac{5}{12} \ (2)$$
$$\frac{12}{5} \ (3) \hfill \frac{144}{25} \ (4)$$

171. To build a capacitor, we have two metal plates, one glass sheet (thickness $0.3\,\text{mm}$, $k=7$), one paraffin layer (thickness $0.1\,\text{cm}$, $k=2$), and one plastic layer (thickness $0.2\,\text{cm}$, $k=5$), and one layer with thickness $0.2\,\text{mm}$ ($k=3$). To maximize the capacitance, which material should we place between the metal plates?
(1) mica (2) glass (3) paraffin (4) plastic

172. In the circuit below, what should the resistance $R$ be so that the output power from the source is maximized, and in this case the current $I$ equals how many amperes?
[Figure: Circuit with EMF $\varepsilon = 24\,\text{V}$, internal resistance $r = 2\,\Omega$, and three resistors $6\,\Omega$, $12\,\Omega$, and $R$ connected in parallel, with current $I$ indicated]
(1) zero and 12
(2) 3 and $4/8$
(3) 4 and 4
(4) 4 and $2/4$
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173. In the circuit below, ammeters $A_1$, $A_2$, $A_3$, and $A_4$ show currents $A$, $2A$, $12A$, and $9A$ respectively. How many amperes of current pass through resistor $R_V$?
[Figure: Circuit diagram with resistors $R_1$, $R_2$, $R_3$, $R_4$, $R_5$, $R_6$, $R_V$ and ammeters $A_1$, $A_2$, $A_3$, $A_4$]

• [(1)] 3
• [(2)] 4
• [(3)] 8
• [(4)] 11

174. In the circuit below, the voltmeter resistance is $10\,\mathrm{k\Omega}$ and the ammeter resistance is $5\,\Omega$. If the voltmeter and ammeter read $12\,\mathrm{V}$ and $0.1\,\mathrm{A}$ respectively, what is the power consumed by resistor $R$ in watts?
[Figure: Circuit with resistor $R$, ammeter $A$, and voltmeter $V$]

• [(1)] $1.15$
• [(2)] $1.5$
• [(3)] $11.5$
• [(4)] $15$

175. Two metals A and B are placed in a magnetic field. The volume of the magnetic domains of metal A changes with difficulty, and after removing the external field it returns to its initial state; but the volume of the domains in metal B changes with ease, and after removing the external field it returns to its initial state. A and B are respectively:

• [(1)] Paramagnetic and hard ferromagnetic
• [(2)] Soft ferromagnetic and paramagnetic
• [(3)] Hard ferromagnetic and soft ferromagnetic
• [(4)] Soft ferromagnetic and hard ferromagnetic

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176- According to the figure below, four thin, parallel, long current-carrying wires, carrying current $I$, are perpendicular to the page and fixed on the page. What are the coordinates of the origin where the magnetic field is zero?
[Figure: Four wires arranged symmetrically; two wires going into the page at positions $(-d, yd)$ and $(yd, -yd)$, and two wires coming out of the page, with spacing $d$ and $yd$ along axes]

• [(1)] $\dfrac{\mu_0 I}{4\pi d}$
• [(2)] $\dfrac{\sqrt{5}\,\mu_0 I}{4\pi d}$
• [(3)] $\dfrac{\sqrt{3}\,\mu_0 I}{4\pi d}$
• [(4)] $\dfrac{\sqrt{2}\,\mu_0 I}{4\pi d}$

177- A coil has $500$ turns and the area of each loop is $120\,\text{cm}^2$. In a uniform magnetic field perpendicular to the plane of the coil, with a constant time base, the EMF varies and the graph of the driving force versus time is as shown in the figure below. What is the magnitude of the magnetic field in Tesla?
[Figure: Graph of $\mathcal{E}$(V) vs $t$(s); sinusoidal wave with period $\dfrac{\pi}{500}$ and amplitude $-90$]

• [(1)] $0.05$
• [(2)] $0.06$
• [(3)] $0.08$
• [(4)] $0.09$

178- A coil has $200$ turns and a magnetic flux of $0.05\,\text{Wb}$ passes through it and both ends of the coil are connected together. If the magnetic flux decreases harmonically to zero and the electrical resistance of the coil is $10\,\Omega$, how many coulombs of electric charge appear in it?

• [(1)] $0.01$
• [(2)] $0.1$
• [(3)] $1$
• [(4)] $10$

184- A tennis ball is thrown vertically from a height of 320 cm and after hitting the ground rises to a height of 125 cm. The ground contact time with the ball is 13 ms. If the contact time of the ball with the ground is 13ms, the magnitude of the average acceleration during contact is how many meters per second squared? (Air resistance is neglected. $g = 10\,\dfrac{\text{m}}{\text{s}^2}$)
(1) 100, upward (2) 100, downward (3) 1000, upward (4) 1000, downward

185- In the figure below, an object is released from the top of an inclined surface and reaches the bottom surface with a speed of $15\,\dfrac{\text{m}}{\text{s}}$. The coefficient of kinetic friction of the object with the surface is how much? $\left(g = 10\,\dfrac{\text{m}}{\text{s}^2},\ \sin 53^\circ = 0.8\right)$
[Figure: inclined plane with $h = 20\,\text{m}$ and angle $53^\circ$]
(1) $\dfrac{3}{4}$ (2) $\dfrac{7}{12}$ [10pt] (3) $\dfrac{1}{3}$ (4) $\dfrac{1}{6}$

186- A horizontal flat surface rotates around a vertical axis and makes 6 complete revolutions per minute. A 5 kg cubic object is placed on this surface at a distance of 2 meters from the axis of rotation and rotates with the surface without sliding. How many newtons of force is applied to the cube? $\left(g = 10\,\dfrac{\text{m}}{\text{s}^2}\right)$
(1) $8$ (2) $2\pi$ (3) $0.7\pi^2$ (4) $0.4\pi^2$

187- The position–time graph of a simple oscillator is shown in the figure below. If the maximum speed of the oscillator at the moment of passing through the center of oscillation is $2\pi\,\dfrac{\text{m}}{\text{s}}$, what is the velocity–time equation in SI?
[Figure: position–time graph of simple harmonic motion with amplitude $A$ and $-\dfrac{\sqrt{3}}{2}A$, period approximately $\dfrac{1}{24}$ s]
(1) $V = 2\pi\cos 20\pi t$
(2) $V = 4\pi\cos 20\pi t$
(3) $V = 2\pi\cos 40\pi t$
(4) $V = 4\pi\cos 40\pi t$
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188- The equation of position -- time of a simple harmonic oscillator in SI is $x = 0.02\sin(100\pi t)$. At the moment $t = \dfrac{1}{150}$ s, the potential energy of the oscillator is how many times its kinetic energy?

(1) $\dfrac{4}{3}$ (2) $\dfrac{3}{2}$ (3) $2$ (4) $4$

189- The equation of lateral energy -- time of a simple harmonic oscillator with mass $100$ g in SI is $K = 45\pi^2 \times 10^{-4}\cos^2(10\pi t)$. How many centimeters is the displacement of the oscillator in the time interval from $t_1 = \dfrac{1}{20}$ s to $t_2 = \dfrac{3}{20}$ s?

(1) zero (2) $2$ (3) $3$ (4) $6$

190- A string of length $80$ cm and mass $8$ g is fixed between two points. The second harmonic frequency of it is $25$ Hz. How many newtons is the tension of the string?

(1) $50$ (2) $500$ (3) $80$ (4) $800$

191- The profile of a transverse wave in a string at the moment $t = 0$ is according to the figure below. In the time interval $0 \leq t \leq \dfrac{1}{80}$ s, how many centimeters is the displacement of point B equal to the displacement of point A?

\begin{minipage}{0.45\textwidth} [Figure: A transverse wave profile showing y(cm) vs x(cm), with velocity $V = 8$ m/s to the right. Point A is at approximately $y = -1$ and point B is at approximately $y = \sqrt{3}$, with the wave showing one full cycle up to $x = 30$ cm.] \end{minipage} \begin{minipage}{0.45\textwidth} \begin{flushright} (1) $\dfrac{3}{4}$
(2) $\dfrac{\sqrt{3}}{2}$
(3) $1$
(4) $\sqrt{3}$ \end{flushright} \end{minipage}

192- In a closed sound tube, the difference between the wavelengths of the fifth and seventh harmonics is how many times the fundamental wavelength of the sound wave?

(1) $\dfrac{3}{25}$ (2) $\dfrac{5}{7}$ (3) $2$ (4) $3$

193- If a sound level of 12 decibels is louder than another sound, the intensity of that sound is how many times the intensity of the other sound? $(\log 2 = 0.3)$

(1) $16$ (2) $32$ (3) $10^2$ (4) $10^{12}$

194- In a medium where the speed of sound propagation is $330\ \dfrac{\text{m}}{\text{s}}$, a sound source moves along a straight path at a speed of how many meters per second so that the wavelength of the sound wave in front of it is $\dfrac{5}{6}$ of the wavelength of the sound wave behind it?

(1) $20$ (2) $22$ (3) $50$ (4) $33$
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195- If we perform Young's double-slit experiment in water instead of air, without changing the light source and without changing the experimental setup, the distance between two consecutive bright fringes will be equal to how much? $\left(n = \dfrac{4}{3}\right)$
\[ \frac{r}{r} \quad (4) \qquad\qquad \frac{r}{f} \quad (3) \qquad\qquad \frac{r}{r} \quad (2) \qquad\qquad \frac{r}{\lambda} \quad (1) \]

196- The diagram below shows the electric field of an electromagnetic wave propagating in vacuum, according to the figure shown. Which statement about this diagram is correct? $\left(c = 3\times10^{8}\ \dfrac{\text{m}}{\text{s}}\right)$
[Figure: Sinusoidal electromagnetic wave with E field on vertical axis and x(m) on horizontal axis, with points O, Y, and B marked]

1. The wavelength is $0.5$ meters.
2. The period of the wave is one second.
3. The wave number is $\pi$ radians per meter.
4. The frequency is $3\times10^{8}$ Hz.