173- A light ray passes through a prism following the path shown in the figure below. Which answer is not correct?

• [(1)] The refractive index of the prism is $\sqrt{2}$.
• [(2)] The deviation angle of the light ray is $135°$.
• [(3)] The critical angle of the prism with respect to air is $45°$.
• [(4)] The speed of light in the prism is $\dfrac{\sqrt{2}}{2}$ times the speed of light in air.

[Figure: A prism with a light ray entering and refracting, with an angle of $135°$ marked]

174- A diverging lens forms a virtual image 2 cm long from an object 4 cm long. If the object is placed 30 cm from the lens, the actual image distance is 8 cm. What is the focal length of this lens?
(1) $10$ (2) $5$ (3) $4$ (4) $2$

175- Two cylinders A and B of equal weight are placed on a horizontal surface. The base area of cylinder B is twice the base area of cylinder A. The pressure exerted by cylinder A is how many times the pressure exerted by cylinder B?
(1) $\dfrac{1}{2}$ (2) $\dfrac{1}{4}$ (3) $2$ (4) $4$

176- In the figure below, mercury is placed on both sides of a U-shaped tube with cross-sectional area $1\ \text{cm}^2$. From one side of the tube, the volume of mercury is $21\ \text{cm}^3$. We pour mercury and raise the air column on the closed side to $15\ \text{cm}$. What is the atmospheric pressure in centimeters of mercury?
(The temperature inside the closed tube is assumed to be constant.)
[Figure: A U-tube with mercury, closed on one side, with height $18\ \text{cm}$ marked]
(1) $73$ (2) $74$ (3) $75$ (4) $76$

177- A piece of metal with density $2.7\ \dfrac{\text{g}}{\text{cm}^3}$ is completely submerged in a container full of alcohol with density $0.8\ \dfrac{\text{g}}{\text{cm}^3}$, and $160\ \text{g}$ of alcohol overflows. How many grams of metal is the piece?
(1) $540$ (2) $450$ (3) $432$ (4) $200$

178- Two conducting spheres A and B with radii $r_A$ and $r_B = 2r_A$, surface charge densities $\sigma_A$ and $\sigma_B = 2\sigma_A$, carry positive electric charge. What percentage of charge should be transferred from the larger sphere to the smaller sphere so that the charge becomes proportional to their radii?
(1) $15$ (2) $25$ (3) $50$ (4) $75$
Workspace for Calculations
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179 – In the circuit shown, the voltage across capacitor $C_1$ is given. How many times is the voltage across $C_3$ compared to the voltage across $C_1$?
\begin{minipage}{0.4\textwidth} [Figure: Series-parallel capacitor circuit with $C_1 = 5\,\mu\text{F}$, $C_2 = 20\,\mu\text{F}$, $C_3$, and $C_4 = 2\,\mu\text{F}$, connected to voltage $V$] \end{minipage} \begin{minipage}{0.55\textwidth}

p{3cm}} (1) $\dfrac{4}{5}$	(2) $\dfrac{1}{5}$
[10pt] (3) $\dfrac{3}{4}$	(4) $\dfrac{1}{4}$

\end{minipage}

180 – In the circuit shown, the maximum tolerable voltage across each capacitor is $60\,\text{V}$. What is the maximum electrical energy that can be stored in these two capacitors, in millijoules?
\begin{minipage}{0.4\textwidth} [Figure: Two capacitors $C_1 = 15\,\mu\text{F}$ and $C_2 = 30\,\mu\text{F}$ connected in series to voltage $V$] \end{minipage} \begin{minipage}{0.55\textwidth}

p{3cm}} (1) $20.5$
[4pt] (2) $24$
[4pt] (3) $40.5$
[4pt] (4) $44$

\end{minipage}

181 – In the circuit shown, all resistors are identical and each resistor can tolerate a maximum power of $20\,\text{W}$. What is the maximum electrical power that can be consumed in this circuit so that no resistor is damaged, in watts?
\begin{minipage}{0.4\textwidth} [Figure: A circuit with resistors in a mixed series-parallel combination connected to voltage $V$] \end{minipage} \begin{minipage}{0.55\textwidth}

p{3cm}} (1) $60$	(2) $40$
[6pt] (3) $36$	(4) $32$

\end{minipage}

182 – The resistance of a copper wire at $20\,^\circ\text{C}$ is $40\,\Omega$. An electric current passes through the wire and due to the temperature increase, its electrical resistance reaches $46.8\,\Omega$. What is the temperature of the wire in this case, in degrees Celsius?
$$\left(\alpha_{\text{Cu}} = 0.0068\,\frac{1}{\text{K}}\right)$$

p{3cm}p{3cm}p{3cm}} (1) $22.5$

(2) $25$

(3) $37.5$

(4) $45$

183 – In the circuit shown, the power consumed by each resistor is equal. What is the equivalent resistance of the circuit, in ohms?
\begin{minipage}{0.4\textwidth} [Figure: Circuit with EMF source $\varepsilon$, and resistors $R_1 = 3\,\Omega$, $R_2$, $R_3$, $R_4$ in a mixed combination] \end{minipage} \begin{minipage}{0.55\textwidth}

p{3cm}} (1) $\dfrac{27}{4}$	(2) $\dfrac{9}{2}$
[10pt] (3) $18$	(4) $9$

\end{minipage}
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184. In the circuit shown, if we gradually increase the variable resistance $R_1$, the EMF decreases and the potential difference across the terminals of the source, and across $R_1$, how do they change? (from right to left)
[Figure: Circuit with EMF source $\varepsilon$, internal resistance $r$, and two resistors $R_1$ (variable) and $R_2$ in series]

• [1)] Increase – Decrease
• [2)] Decrease – Increase
• [3)] Increase – Increase
• [4)] Decrease – Decrease

185. In the figure, two long parallel wires carry electric currents of equal magnitude in opposite directions through point I. The magnetic field at point M, equidistant from the two wires, is:
[Figure: Two parallel wires separated by distance $2d$, point M is at distance $d$ from each wire and distance $a$ below the midpoint]
$$\frac{2\mu_0 Id}{\pi(2a^2+d^2)} \quad (1) \qquad \frac{\mu_0 Id}{\pi(2a^2+d^2)} \quad (2)$$
$$\frac{\mu_0 Ia}{\pi(4d^2+a^2)} \quad (3) \qquad \frac{2\mu_0 Ia}{\pi(4d^2+a^2)} \quad (4)$$

186. A proton and an alpha particle $\alpha$ with equal kinetic energies enter a magnetic field of magnitude $B$ and move in circular paths perpendicular to the magnetic field. Which of the following statements about these two particles is correct? (Mass of alpha particle $\alpha$ is 4 times the mass of the proton.)

• [1)] The speed of $\alpha$ is 2 times the speed of the proton.
• [2)] The momentum of the proton equals the momentum of particle $\alpha$.
• [3)] The radius of the path of $\alpha$ equals the radius of the path of the proton.
• [4)] The electromagnetic force on the proton is 2 times the electromagnetic force on particle $\alpha$.

187. The equation of electric current passing through a coil in SI units is $I = 2\sqrt{2}\sin 300t$. If the maximum energy stored in the coil is $0.8$ joules, what is the equation of the self-induced EMF of the coil in SI units?

• [1)] $\varepsilon = 120\sqrt{2}\cos(300t - \pi)$
• [2)] $\varepsilon = 120\sqrt{2}\sin(300t - \pi)$
• [3)] $\varepsilon = 120\sin 300t$
• [4)] $\varepsilon = 120\cos 300t$

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188- The velocity-time graph of a simple harmonic oscillator is shown below. In the time interval $t_1$ to $t_2$, the average velocity of the oscillator is how many centimeters per second?
\begin{minipage}{0.45\textwidth} [Figure: velocity-time graph of a simple harmonic oscillator, with $V$ axis in $\text{Cm/s}$, showing amplitude $10\pi$ and $-5\pi$, with time points $t_1$ and $t_2$ marked] \end{minipage} \begin{minipage}{0.45\textwidth}

• [(1)] $2/5\sqrt{3}$
• [(2)] $2/5\pi$
• [(3)] $7/5\pi$
• [(4)] $7/5\sqrt{3}$

\end{minipage}

189- A mass-spring oscillator oscillates on a frictionless horizontal surface with amplitude $A_1$ and frequency $f_1$. At the moment when the oscillator is at the farthest distance from the center of oscillation, $\frac{3}{4}$ of the mass separates and the remaining mass attached to the spring continues to oscillate. If in this new state the frequency is $f_2$ and the amplitude is $A_2$, the ratios $\dfrac{f_2}{f_1}$ and $\dfrac{A_2}{A_1}$ from right to left are respectively:
(1) 1 and 1 (2) 1 and 2 (3) 1 and 1 (4) 2 and 2

190- A transverse wave is propagating in a rope. In this regard, which option is not correct?

1. [(1)] The distance between any two points with opposite phase is equal to half the wavelength.
2. [(2)] The phase difference of two points in phase is an even multiple of $\pi$.
3. [(3)] The phase difference of two points with opposite phase is an odd multiple of $\pi$.
4. [(4)] The distance between two points in phase is equal to the wavelength.

191- A guitar string closed on both ends has a mass of 4 grams, a cross-sectional diameter of 1 millimeter, and a length of 40 centimeters. If the string is stretched with a force of 30 Newtons, what is the fundamental frequency? $(\pi = 3)$
(1) 125 (2) 250 (3) 375 (4) 500

192- The figure shows a wave pattern at $t = 0$. At the moment $t = \dfrac{1}{300}$ s, the displacement of particle A is how many times the displacement of particle B?
\begin{minipage}{0.45\textwidth} [Figure: wave pattern at $t=0$, $y$-axis in Cm with amplitude 1, $x$-axis in Cm up to 30, wave moving with $V = 8\,\text{m/s}$ to the right, particle A at $y=1$ and particle B at $y=-1$] \end{minipage} \begin{minipage}{0.45\textwidth}

• [(1)] 1
• [(2)] $\dfrac{1}{2}$
• [(3)] $\dfrac{\sqrt{3}}{2}$
• [(4)] $\dfrac{\sqrt{2}}{2}$

\end{minipage}
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193- Air inside a closed tube, open at both ends, forms 3 nodes in the tube. In this case, if the sequential distance of 2 nodes is $25\ \text{cm}$, what is the fundamental frequency of the tube? (Speed of sound in air inside the tube is $340\ \dfrac{\text{m}}{\text{s}}$.)
(1) $170$ (2) $340$ (3) $510$ (4) $680$

194- A stationary car horn emits a sound wave of $660\ \text{Hz}$. If we approach this stationary car at a speed of $36\ \dfrac{\text{km}}{\text{h}}$, how many hertz do we hear the horn? $\left(\text{speed of sound in air} = 330\ \dfrac{\text{m}}{\text{s}}\right)$
(1) $640$ (2) $660$ (3) $680$ (4) $730$

195- In radar, which waves are used to detect aircraft or ships?
(1) Gamma rays (2) Ultraviolet rays (3) Infrared waves (4) Radio waves

196- In Young's experiment, the time difference for light to travel from two slits to the center of the fifth dark fringe is $6\times10^{-15}$ seconds. What is the wavelength of the light used in the experiment in nanometers? $\left(C = 3\times10^{8}\ \dfrac{\text{m}}{\text{s}}\right)$
(1) $550$ (2) $500$ (3) $450$ (4) $400$

197- If Planck's constant is $6.6\times10^{-34}\ \text{J}\cdot\text{s}$, what is the ratio in electron volt seconds? $\left(e = 1.6\times10^{-19}\ \text{C}\right)$
(1) $\dfrac{\lambda}{33}\times10^{15}$ (2) $\dfrac{33}{\lambda}\times10^{-15}$ (3) $\dfrac{33}{\lambda}\times10^{-15}$ (4) $\dfrac{\lambda}{33}\times10^{15}$