160- In the figure, a pulley, a mass, and a frictionless string are shown. If the system is released from rest, a 2 kg weight moves how many centimeters in $0.55$ seconds? $\left(g = 10\,\dfrac{\text{m}}{\text{s}^2}\right)$
[Figure: Atwood machine with two masses each labeled 2 kg connected by a string over a pulley fixed to a ceiling.]
(1) $27.5$ (2) $42.5$ (3) $55$ (4) $85$
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161. A body of mass $4\,\text{kg}$ slides down a frictionless inclined surface that makes an angle $\alpha$ with the horizontal, with initial speed $4\,\dfrac{\text{m}}{\text{s}}$ upward along the surface. If the speed of the body reaches zero after $0.5\,\text{s}$, how large is the force (in Newtons) that the body exerts on the surface? $\left(g = 10\,\dfrac{\text{m}}{\text{s}^2}\right)$
$32\ (1$ $24\ (2$ $8\ (3$ $6\ (4$

162. In the figure below, an airplane with speed $150\,\dfrac{\text{m}}{\text{s}}$ is traveling in a circular path. The wing of the airplane makes a horizontal angle of $37°$ with the surface. What is the radius of the path in kilometers? $\left(\tan 37° = \dfrac{3}{4},\ g = 10\,\dfrac{\text{m}}{\text{s}^2}\right)$
[Figure: airplane banking at angle $\theta$]
\begin{flushright} $0.3\ (1$ $3\ (2$ $30\ (3$ $300\ (4$ \end{flushright}

163. A particle undergoes uniform circular motion in the $xoy$ plane, accelerating in the $\hat{j}$ direction, with period $4\,\text{s}$. If at a given moment the acceleration vector is $\vec{a} = 2\vec{i} - 2\vec{j}$, what is the position vector of the particle $1.5\,\text{s}$ later? (Units are in SI.)
$-2\vec{i} + 2\vec{j}\ (1$ $2\vec{i} + 2\vec{j}\ (2$ $-2\sqrt{2}\,\vec{j}\ (3$ $2\sqrt{2}\,\vec{j}\ (4$

165. According to the figure below, a monochromatic light ray enters a prism from air and after refraction exits the prism. Which of the following statements is not correct? $\left(\dfrac{\sqrt{2}}{2} = 0.7\right)$
[Figure: prism with apex angles $45°$ on each side, rays at $3°$ and $3°$ from normal, normal lines shown]

1. The angle of deviation is $6°$.
2. The critical angle of the prism is $45°$.
3. The refractive index of the prism is $\sqrt{2}$.
4. The speed of light in the prism is $0.7$ times the speed of light in air.

Calculation Space
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166- A ball is placed at the midpoint between a spherical lamp and a wall, and the diameter of the ball equals the diameter of the lamp. The width of the shadow formed by the ball on the wall is how many times the diameter of the ball?
(1) $1$ (2) $2$ (3) $3$ (4) $4$

167- The figure shows the reflection from the surface of a convex mirror. $F$ and $C$ are the focus and center of the mirror. What is the correct relationship between $\alpha$ and $\beta$?
[Figure: A convex mirror with an incident ray making angle $\alpha$ with the principal axis and reflected ray making angle $\beta$, with points F and C marked on the axis]

• [(1)] $2\alpha < \beta < 3\alpha$
• [(2)] $\alpha < \beta < 2\alpha$
• [(3)] $\beta = 2\alpha$
• [(4)] $\beta = 3\alpha$

168- An object is placed $20$ cm in front of a concave mirror whose radius of curvature is $40$ cm. If we move the object away from the mirror and go to very far distances, the image moves how many centimeters?
(1) $5$ (2) $20$ (3) $25$ (4) $15$

169- The volume of an object is $2.4 \times 10^{-3}$ m$^3$. What instrument was used to measure this?
(Measurement precision: ruler $0.1$ cm, vernier caliper $0.01$ cm, micrometer $0.001$ mm, and tape measure $0.1$ cm.)
(1) Vernier caliper (2) Micrometer (3) Ruler (4) Tape measure

170- In the figure of a U-tube, the pressure difference at point A and the air pressure is how many kilopascals?
$$\left(g = 10\,\frac{\text{N}}{\text{kg}},\ \rho_{\text{water}} = 1\,\frac{\text{g}}{\text{cm}^3},\ \rho_{\text{mercury}} = 13.6\,\frac{\text{g}}{\text{cm}^3}\right)$$
[Figure: A U-tube with water on one side and mercury on the other; point A is marked on the water side; the water column is $40$ cm and mercury column is $60$ cm]

• [(1)] $13.6$
• [(2)] $136$
• [(3)] $130$
• [(4)] $60$

171- Cylinder A is full of water. The force exerted by the water on the base of cylinder A is $F_A$ and the pressure at the base of cylinder A is $P_A$. If cylinder B has dimensions equal to half those of cylinder A and we fill it with water, the force and pressure are $F_B$ and $P_B$ respectively. The ratios $\dfrac{F_A}{F_B}$ and $\dfrac{P_A}{P_B}$, from right to left, are respectively:
(1) $2$ and $2$ (2) $4$ and $2$ (3) $8$ and $8$ (4) $2$ and $8$
Calculation Space
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172. On a winter day, the outdoor temperature is $-5$ degrees Celsius and the indoor temperature is $20$ degrees Celsius. If we increase the indoor temperature by $25$ degrees Celsius and keep it at $25$ degrees Celsius, the rate of heat loss through conduction changes by how much?
(1) $\dfrac{6}{5}$ (2) $\dfrac{5}{4}$ (3) $\dfrac{4}{3}$ (4) $\dfrac{7}{5}$

173. According to the figure below, two metal plates with thermal conductivities $k_1 = 400\,\dfrac{\text{W}}{\text{m.k}}$ and $k_2 = 800\,\dfrac{\text{W}}{\text{m.k}}$ and equal thickness are glued together. The temperatures of the outer surfaces of the plates are $\theta_1 = 0\,^\circ\text{C}$ and $\theta_2 = 90\,^\circ\text{C}$. In steady-state conditions, the temperature at the junction of the two plates is how many degrees Celsius?
[Figure: Two rectangular plates placed side by side, labeled with $k_1$, $k_2$, $\theta_1$, and $\theta_2$]

• [(1)] $10$
• [(2)] $15$
• [(3)] $25$
• [(4)] $30$

174. In the figure, container A has a volume of 2 liters and contains oxygen gas at a temperature of $47\,^\circ\text{C}$ and a pressure of 4 atm, and container B has a volume of 5 liters and is completely empty. If we open the valve connecting the two containers and bring the temperature and pressure of the gas in the containers to 7 degrees Celsius, what will the pressure of the gas be in atm?
[Figure: Two containers A and B connected by a valve]

• [(1)] $0.75$
• [(2)] $1.25$
• [(3)] $1$
• [(4)] $2$

175. In the table below, which of the following words is appropriate for X and Y from right to left?

Process type	Pressure	Volume	Internal Energy
Irreversible	Decrease	Y	X

• [(1)] Decrease, Increase
• [(2)] Increase, Increase
• [(3)] Increase, Decrease
• [(4)] Decrease, Decrease

Calculation Space
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176. If the coefficient of performance of refrigerator (1) is 1.5 times the coefficient of performance of refrigerator (2), and both have equal time periods, while both refrigerators are running simultaneously, the heat that refrigerator (1) releases to the outside is how many times the heat that refrigerator (2) releases to the outside?

p{6cm}} (2) $\dfrac{4}{3}$	(1) $\dfrac{3}{2}$
[10pt] (4) depends on the size of the coefficient of performance of the refrigerators	(3) $\dfrac{5}{4}$

177. Two small identical metal spheres that have equal electric charges are 30 cm apart. The attractive force between them is 4 Newtons. If we bring the two spheres into contact and then separate them, the electric charge of each sphere will be $+3\mu C$. What was the initial charge of the spheres? (in microcoulombs) $\left(k = 9\times10^9\ \dfrac{\text{N.m}^2}{\text{C}^2}\right)$

p{3cm} p{3cm} p{3cm}} (1) $12$ and $-6$

(2) $-4$ and $10$

(3) $9$ and $-3$

(4) $8$ and $-2$

178. By partially discharging an electric capacitor, the potential difference across it decreases by 80 percent. The energy of this capacitor decreases by what percent?

p{3cm} p{3cm} p{3cm}} (1) $50$

(2) $64$

(3) $80$

(4) $96$

179. In figures (a) and (b), the capacitors and batteries are identical. If the charge on each capacitor in figure (a) is $q_1$, and we name the charge on each capacitor in figure (b) $q_2$, what is the ratio $\dfrac{q_1}{q_2}$?

[Figure: Two circuit diagrams labeled (a) and (b), each containing capacitors and a battery. In (a) capacitors are in series; in (b) capacitors are in parallel.]

p{6cm}}	(1) $1$
[6pt]	(2) $2$
[6pt]	(3) $\dfrac{1}{2}$
[6pt]	(4) $\dfrac{1}{4}$

180. In the circuit shown, when the external resistance is 8 ohms, the useful power delivered equals $P_1$. The internal resistance of the battery is $r = 4\ \Omega$. To what value should we change the external resistance so that the useful power delivered is again equal to $P_1$?

[Figure: A circuit with a battery of internal resistance $r = 4\ \Omega$ and an external resistor.]

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

(2) $2$

(3) $4$

(4) $6$

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181- What is the minimum number of $4\,\Omega$ resistors that must be connected together so that, from a $12\,\text{V}$ power source, an electric current of $15\,\text{A}$ is obtained?
(1) $3$ (2) $4$ (3) $5$ (4) $6$

182- In the circuit shown, $V_A - V_B$ is how many volts? (Internal resistances of the batteries are negligible.)
[Figure: Circuit with two batteries $\varepsilon_1 = 10\,\text{V}$ and $\varepsilon_2 = 10\,\text{V}$, resistors $6\,\Omega$, $4\,\Omega$, $3\,\Omega$, between nodes A and B.]
(1) $4$ (2) $-4$ (3) $16$ (4) $-16$

183- In the circuit shown, when both switches are open or both are closed, the ammeter reads $0.2\,\text{A}$. What is the resistance $R$?
[Figure: Circuit with resistors $30\,\Omega$, $40\,\Omega$, $30\,\Omega$, switches $k_1$ and $k_2$, resistor $R$, battery $\varepsilon$ with internal resistance $r = 10\,\Omega$.]
(1) $60$ (2) $40$ (3) $15$ (4) $10$

184- The number of rectangular loops of a coil equals the number of turns of a solenoid, and the electric current through them is equal. If the magnetic field created inside the solenoid equals the magnetic field at the center of the coil, what is the length of the solenoid in terms of the coil's diameter?
(1) $1$ (2) $2$ (3) $\dfrac{1}{2}$ (4) $\dfrac{1}{4}$

185- The figure shows long, straight, parallel wires perpendicular to the page, with the direction and magnitude of the currents indicated. What is the direction of the magnetic force entering the center of the square?
[Figure: Square arrangement of four wires at corners; $I_1 = 2I$ (top-left, out of page), $I_2 = I$ (top-right, out of page), $I_3 = 2I$ (bottom-left, into page), $I_4 = I$ (bottom-right, into page).]
(1) $\leftarrow$ (2) $\rightarrow$ (3) $\downarrow$ (4) $\uparrow$
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