168. A body of mass $m$ is connected to a spring with constant $k$ and oscillates. The period of oscillation is $0.9\pi$ seconds. If the mass of the body decreases by $190\,\text{g}$ and the period of oscillation becomes $0.09\pi$ seconds, $k$ is how many newtons per meter?
(1) $2$ (2) $4$ (3) $20$ (4) $40$

169. A simple pendulum completes 40 full oscillations in 72 seconds. How should we change the length of the pendulum so that it completes 45 full oscillations in the same time? $\left(g = \pi^2\,\dfrac{\text{m}}{\text{s}^2}\right)$
(1) Decrease by 9\,cm. (2) Increase by 9\,cm.
(3) Decrease by 17\,cm. (4) Increase by 17\,cm.
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170. Two people are at distances $d_1$ and $d_2$ from a sound source. A person who is at distance $d_1$ hears the sound 18 decibels louder. $\log 2 = 0.3$. Which of the following is $\dfrac{d_2}{d_1}$? (Assume no energy is absorbed by the medium.)
(1) $4$ (2) $8$ (3) $9$ (4) $16$

171. The figure below shows the transverse wave on a rope at moment $t = 0$, propagating with speed $10\ \dfrac{\text{m}}{\text{s}}$. What is the distance that particle $M$ travels during the time interval $t_1 = 0.015\ \text{s}$ to $t_2 = 0.058\ \text{s}$, in centimeters?
[Figure: Transverse wave on a rope; y-axis in cm with amplitude $a$ and $-r$; x-axis in cm; point M is marked on the wave; wavelength marking of $120$ cm is shown.]
(1) $3$
(2) $6$
(3) $9$
(4) $12$

172. According to the figure below, ray $SI$ hits mirror (1) at angle of incidence $i$. The angle between ray $SI$ and reflected ray from mirror (2), $\gamma = 120°$. If angle $i$ increases by $20°$, how does $\gamma$ change?
[Figure: Two mirrors; ray SI incident on mirror (1) at angle $\alpha$; reflected ray hitting mirror (2); $\gamma = 120°$ is marked.]

1. [(1)] Increases by $40°$.
2. [(2)] Increases by $20°$.
3. [(3)] Decreases by $20°$.
4. [(4)] Remains constant.

173. An object is placed 120 cm in front of a lens and the magnification of the lens is $0.4$. How should the object be moved along the principal axis so that the image length becomes half the object length?

1. [(1)] Move 30 cm away from the lens.
2. [(2)] Move 20 cm closer to the lens.
3. [(3)] Move 40 cm away from the lens.
4. [(4)] Move 40 cm closer to the lens.

174. According to the figure below, a light ray enters medium (2) from medium (1). The wavelength of light in medium (2) is how many times the wavelength of light in medium (1)?
[Figure: Light ray passing from medium $n_1$ to medium $n_2$; angle of incidence $60°$ and angle of refraction $15°$ are shown; normal line indicated.]
(1) $\sqrt{2}$ [4pt] (2) $\dfrac{\sqrt{3}}{2}$ [4pt] (3) $2$ [4pt] (4) $\dfrac{1}{2}$
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175. The wavelength of the fifth line of the hydrogen atom spectrum in the Balmer series ($n' = 2$) is approximately how many nanometers, and in which region of the electromagnetic spectrum does it fall? $\left(R = 0.0110 \text{ (nm)}^{-1}\right)$
(1) 433, visible (2) 433, infrared (3) 396, red (4) 396, infrared

176. The work functions of metals A and B are $4.5\text{ eV}$ and $3\text{ eV}$ respectively. If light with wavelength $150\text{ nm}$ shines on both metals, the photoelectric kinetic energy of metal A's electrons is what percent less than the photoelectric kinetic energy of metal B's electrons? $$\left(c = 3\times10^{8}\ \frac{\text{m}}{\text{s}},\ h = 4\times10^{-15}\ \text{eV.s}\right)$$
(1) $30\%$ (2) $40\%$ (3) $60\%$ (4) $70\%$

177. In heavy nuclei, a proton with electrostatic force, ............, and with nuclear force ............
(1) Only nearby protons repel it --- all nucleons inside the nucleus attract it.
(2) All nucleons inside the nucleus repel it --- only nearby nucleons attract it.
(3) Only nearby neutrons and protons repel it --- all nucleons inside the nucleus attract it.
(4) All protons inside the nucleus repel it --- only nearby nucleons attract it.

178. The half-life of polonium-A is 8 years. What percentage of this material remains after 32 years?
(1) $16\%$ (2) $24\%$ (3) $32\%$ (4) $64\%$

179. If the magnitude of the electric field produced by a point charge at 30 cm is $1.6\times10^{4}\ \dfrac{\text{N}}{\text{C}}$ less than the magnitude of the electric field at 10 cm from it, the charge of that particle at a distance of 1 meter is how many coulombs?
(1) $90$ (2) $120$ (3) $180$ (4) $240$

180. In the figure below, the resultant electric force on each of the charges is zero. The ratios $\dfrac{q_3}{q_2}$ and $\dfrac{x}{r}$ from right to left are:
[Figure: Three charges on a line: $q_2$, then $q_3$ at distance $x$, then $q_1 = -\dfrac{4}{5}q_2$ at distance $r$]
(1) $9\ ,\ \dfrac{3}{2}$ (2) $-9\ ,\ \dfrac{3}{2}$ (3) $9\ ,\ 2$ (4) $-9\ ,\ 2$

181. In the figure below, in a uniform electric field $E = 10^{5}\ \dfrac{\text{N}}{\text{C}}$, a point charge $q = -5\ \mu\text{C}$ is moved along the shown path from point A to point B. In this transition, the electric potential energy of this charged particle changes by how many joules?
(1) $+0.15$
(2) $-0.15$
(3) $+0.10$
(4) $-0.10$
[Figure: Uniform electric field $\vec{E}$ pointing right; path from A to B in a region 20 cm tall and 30 cm wide, with A located 5 cm from the bottom-left, B on the right side; horizontal displacement is 30 cm, vertical dimension shown as 20 cm and 5 cm.]
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182. A capacitor with capacitance $12\,\mu\text{F}$ and electric potential difference between its two plates is $V_1$. If $-6\,\mu\text{C}$ of charge is transferred from the negative plate to the positive plate, the energy stored in it decreases by $28.5\,\mu\text{J}$. $V_1$ is how many volts?
(1) $5$ (2) $10$ (3) $15$ (4) $20$

183. In the circuit below, all capacitors are identical and the switch is initially open. When the switch is closed, the charge on capacitor $C_5$ becomes equal to what fraction of $C_\Delta$?
[Figure: Circuit with capacitors $C_1$, $C_2$, $C_3$, $C_4$, $C_5$, $C_6$ connected with a voltage source $V$ and a switch]
$$\text{(1)}\;\frac{11}{12} \qquad \text{(2)}\;\frac{11}{15} \qquad \text{(3)}\;\frac{2}{5} \qquad \text{(4)}\;\frac{3}{10}$$

184. The figure below shows part of an electric circuit. The energy consumed in resistor $R$ in $25$ minutes is how many kilojoules?
[Figure: Circuit segment with $10\,\Omega$ resistor, resistor $R$, $4\,\text{A}$ current source, $1.6\,\text{A}$ branch current, and $5\,\Omega$ resistor]
(1) $4.8$ (2) $9.6$ (3) $19.2$ (4) $27.4$

185. In the circuit shown, what voltage does the ideal voltmeter read?
[Figure: Circuit with $\varepsilon_1 = 16\,\text{V}$, $r_1 = 2\,\Omega$; $\varepsilon_2 = 6\,\text{V}$, $r_2 = 1\,\Omega$; $\varepsilon_3 = 4\,\text{V}$, $r_3 = 0$; resistors $4\,\Omega$, $5\,\Omega$, $6\,\Omega$, $3\,\Omega$; voltmeter between points $a$ and $b$]
(1) $0.6$ (2) $2.4$ (3) $5.2$ (4) $6.4$

186. In the circuit below, when the switch is closed, how does the potential difference across the $5\,\Omega$ resistor change?
[Figure: Circuit with $5\,\Omega$, $30\,\Omega$, $4\,\Omega$ resistors, switch $k$, battery $\varepsilon = 18\,\text{V}$, $r = 1\,\Omega$]

1. [(1)] Decreases by $8$ volts.
2. [(2)] Increases by $8$ volts.
3. [(3)] Decreases by $1$ volt.
4. [(4)] Increases by $1$ volt.

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187- The electrical resistance of a wire is $6\,\Omega$. We cut $\dfrac{3}{4}$ of the wire and set it aside, and connect $\dfrac{1}{4}$ of the remaining wire to the device, stretching it until its length equals the original wire's length. With temperature held constant, what is the resistance of the new wire?
(1) $9$ (2) $12$ (3) $18$ (4) $24$

188- The figure below shows the cross-section of two long parallel wires perpendicular to the page, carrying equal currents in the directions shown. At point M, what is the direction of the net (pure) magnetic field?

• [(1)] In the direction of the $x$-axis
• [(2)] In the direction of the $y$-axis
• [(3)] Opposite to the $x$-axis
• [(4)] Opposite to the $y$-axis

[Figure: Two long parallel wires shown in cross-section. Wire $I_1$ (current out of page) is at upper left, wire $I_2$ (current into page) is at lower left. A coordinate system with $x$ and $y$ axes is shown, with point M on the $x$-axis to the right of the origin.]

189- A loop with area $200\,\text{cm}^2$ is placed inside a uniform magnetic field of magnitude $B = 0.004\,\text{T}$, and the field lines make an angle of $60°$ with the plane of the loop. What is the magnetic flux through the loop?
(1) $7\times10^{-5}$ (2) $4\times10^{-5}$ (3) $4\sqrt{3}\times10^{-5}$ (4) $4\sqrt{3}\times10^{-5}$

190- The graph of a sinusoidal alternating current is shown below. What is the value of the current at the moment $t = \dfrac{1}{3200}\,\text{s}$?

• [(1)] $2.5$
• [(2)] $2.5\sqrt{2}$
• [(3)] $5$
• [(4)] $5\sqrt{2}$

[Figure: Graph of $I\,(\text{A})$ vs $t\,(\text{s})$. The current is sinusoidal with amplitude $-5\sqrt{2}$ (minimum shown on $y$-axis) and period marked at $t = \dfrac{1}{320}$ on the $x$-axis.]

Calculation Space
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191. In the figure below, an athlete throws a ball with an initial speed of $6\,\dfrac{\text{m}}{\text{s}}$ and the magnitude of the ball's velocity at the moment of entering the basket is $5\,\dfrac{\text{m}}{\text{s}}$. The distance from the throwing point to the surface of the ground $(h_1)$ is how many meters? (Air resistance is negligible and $g = 10\,\dfrac{\text{m}}{\text{s}^2}$.)
[Figure: A basketball player throwing a ball toward a basket; $h_1 = ?$ and $h_t = 3/\cdot\,\text{m}$ are labeled.]

• [(1)] $2/45$
• [(2)] $2/46$
• [(3)] $2/55$
• [(4)] $2/64$

192. A water pump transfers $3$ cubic meters of river water per minute to points whose height above the river water surface is $24$ meters. If the input power of the pump is $20$ kilowatts, what is the efficiency of the pump in percent? $$\left(g = 10\,\frac{\text{m}}{\text{s}^2},\quad \rho_{\text{water}} = 1\,\frac{\text{g}}{\text{cm}^3}\right)$$

• [(1)] $70$
• [(2)] $60$
• [(3)] $40$
• [(4)] $30$