173. An oscillator with mass $100\,\text{g}$ is attached to a spring with spring constant $40\,\dfrac{\text{N}}{\text{m}}$, placed on a horizontal surface, and performs simple harmonic motion without friction. If the total mechanical energy of the oscillator equals $8\,\text{mJ}$, and the mechanical energy of the oscillator equals the tangential kinetic energy, what is the speed of the oscillator at that moment (in meters per second)?
$$\frac{\sqrt{2}}{10} \;(1) \qquad \frac{\sqrt{2}}{5} \;(2) \qquad 10\sqrt{2} \;(3) \qquad 20\sqrt{2} \;(4)$$

174. A $200\,\text{W}$ lamp emits violet light with wavelength $400\,\text{nm}$. Another $200\,\text{W}$ lamp emits yellow light with wavelength $600\,\text{nm}$. How many photons does the yellow lamp emit per second compared to the violet lamp during the same time?
$$\frac{2}{3} \;(1) \qquad 1 \;(2) \qquad \frac{3}{2} \;(3) \qquad 2 \;(4)$$

175. The work function of a metal is $4.14\,\text{eV}$. What is the maximum wavelength of light to eject electrons from the surface of this metal in nanometers?
$$\left(h = 4.14\times10^{-15}\,\text{eV.s} \text{ and } C = 3\times10^{8}\,\frac{\text{m}}{\text{s}}\right)$$
$$300 \;(1) \qquad 400 \;(2) \qquad 500 \;(3) \qquad 600 \;(4)$$

176. In the reaction ${}^{237}_{92}\text{X} \rightarrow \text{Y} + 3\alpha + \beta^{-}$, how many nucleons does $\text{Y}$ have?
$$224 \;(1) \qquad 225 \;(2) \qquad 226 \;(3) \qquad 228 \;(4)$$

177. The radioactive decay diagram of a sample of protium is shown below as a function of time. What is the half-life of this material in days?
[Figure: Radioactive decay graph showing number of nuclei $N$ vs. time (days). The y-axis shows $N_\circ$ and $\dfrac{31}{32}N_\circ$; the x-axis shows time in days with a marked point at 125.]

• [(1)] 5
• [(2)] 25
• [(3)] 50
• [(4)] 62.5

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178. In the figure below, a charge $q = -50\,\mu\text{C}$ enters point A with an electric potential of 120 V and the electric potential energy changes by $5\,\text{mJ}$. What is the electric potential at point B?
[Figure: Point A with arrow indicating direction of $\vec{E}$, point B below]

• [(1)] 70
• [(2)] 110
• [(3)] 130
• [(4)] 220

179. Four charged particles are placed at the corners of a square with side $20\,\text{cm}$ as shown in the figure below. If the net electric force on $q_2$ in SI units is $\vec{F} = -9\hat{i}$, how many microcoulombs is $q_2$?
$$\left(k = 9\times10^9\,\frac{\text{N}\cdot\text{m}^2}{\text{C}^2}\right)$$
[Figure: Square with charges at corners: $q_1 = 4\,\mu\text{C}$ (top left), $q_2 = -4\,\mu\text{C}$ (top right), $q_3$ (bottom left), $q_4 = -4\,\mu\text{C}$ (bottom right), with coordinate axes $x$ and $y$ shown]

• [(1)] $-8\sqrt{2}$
• [(2)] $-4$
• [(3)] $4$
• [(4)] $8\sqrt{2}$

180. If the magnitude of each of two point charges is tripled and the distance between them is also tripled, how many times does the electric force between them become?

• [(1)] $\dfrac{1}{3}$
• [(2)] $1$
• [(3)] $3$
• [(4)] $9$

181. Three fixed point charges are arranged as shown in the figure below. The electric field at point O due to the three charges is $100\,\dfrac{\text{N}}{\text{C}}$.
$$\left(k = 9\times10^9\,\frac{\text{N}\cdot\text{m}^2}{\text{C}^2}\right)$$
How many nanocoulombs can $q_2$ be?
[Figure: Three charges on a line: $q_1 = 8\,\text{nC}$ at left, $q_2 = ?$ in middle, $q_3 = -2\,\text{nC}$ at right, point O at far right; distances of 10 cm between each]

• [(1)] $+4$
• [(2)] $+2$
• [(3)] $-2$
• [(4)] $-4$

182. A capacitor whose voltage can be adjusted is connected to a battery. If the voltage across the capacitor is changed from 2 V to 15 V, how many times does the stored energy in it become?

• [(1)] $\dfrac{3}{4}$
• [(2)] $\dfrac{2}{3}$
• [(3)] $\dfrac{9}{16}$
• [(4)] $\dfrac{3}{16}$

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183. What is a thermistor?
(1) A type of diode that is sensitive to light and heat.
(2) A type of diode used as a thermometer.
(3) A type of resistor whose electrical resistance at temperature is approximately zero.
(4) A type of resistor whose electrical resistance at temperature differs significantly from ordinary resistances.

184. In the circuit below, the equivalent resistance between points M and N is $\dfrac{R}{2}$. How many ohms is $R$?
[Figure: Circuit with an $18\,\Omega$ resistor in the top branch, three resistors $R$ in series in the middle branch between points M and N, and one resistor $R$ in the bottom branch, all connected in parallel between M and N.]

• [(1)] $18$
• [(2)] $12$
• [(3)] $6$
• [(4)] $3$

185. The figure below shows the relationship between the current passing through resistors A and B and the potential difference across them. How many times is resistance B compared to resistance A?
[Figure: $I$-$V$ graph showing two lines through the origin; line B has a steeper slope than line A.]

• [(1)] $\dfrac{4}{9}$
• [(2)] $\dfrac{2}{3}$
• [(3)] $\dfrac{3}{2}$
• [(4)] $\dfrac{9}{4}$

186. In the circuit below, what does the voltmeter read?
[Figure: A circuit with a battery of EMF $\varepsilon = 12\,\text{V}$ and internal resistance $r = 6\,\Omega$, connected to an open switch and a voltmeter V across the terminals.]

• [(1)] zero
• [(2)] $2$
• [(3)] $6$
• [(4)] $12$

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\begin{flushright} Physics 121-A Page 16 \end{flushright}

187. A flat coil consisting of 50 loops with surface area of each loop $64\pi \, \text{cm}^2$ is placed in a magnetic field. If a current of 8 A passes through it, what is the magnitude of the magnetic field at the center of the coil? $\left(\mu_\circ = 4\pi \times 10^{-7} \, \dfrac{\text{T.m}}{\text{A}}\right)$
(1) $10^{-3}$ (2) $10^{-3}\pi$ (3) $1.6 \times 10^{-3}$ (4) $2 \times 10^{-3}\pi$

188. An electron with velocity $\vec{V}$ moves in a magnetic field, perpendicular to the field. If the figure below shows the direction of the magnetic field $(\vec{B})$ and the direction of the force $(\vec{F})$ applied to the electron, what is the direction of $\vec{V}$?
\begin{minipage}{0.2\textwidth} [Figure: $\vec{B}$ pointing upward, $\vec{F}$ pointing into the page ($\otimes$)] \end{minipage} \begin{minipage}{0.6\textwidth} (1) $\odot$
(2) $\otimes$
(3) $\rightarrow$
(4) $\leftarrow$ \end{minipage}

189. The equation of the magnetic flux passing through a coil with 60 loops is, in SI units: $\phi = 4\times10^{-3}\cos100\pi t$
The average magnitude of the induced EMF in the coil over the time interval $t_1 = \dfrac{1}{400}\,\text{s}$ to $t_2 = \dfrac{1}{100}\,\text{s}$ is how many volts?
(1) $2.4$ (2) $4.8$ (3) $24$ (4) $48$

190. A wire segment $MN$ on conductors $U$ of rail $MN$ moves with constant velocity $V$ in time interval $\Delta t$ from position $MN$ to position $M'N'$. If the induced EMF is 0.15 V and the velocity of the wire segment is how many meters per second, and the direction of the induced current in the wire is:
[Figure: A rectangular rail with magnetic field $\vec{B}$ directed out of the page ($\odot$), $B = 0.12\,\text{T}$, rail width $25\,\text{cm}$, wire segment moving from $MN$ to $M'N'$]
(1) 5 from N toward M
(2) 5 from M toward N
(3) 7.5 from N toward M
(4) 7.5 from M toward N
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191. A metallic cubic block with dimensions $5\,\text{cm} \times 4\,\text{cm} \times 2\,\text{cm}$ and density $8\,\dfrac{\text{g}}{\text{cm}^3}$ is placed on a horizontal surface on one of its faces. What is the maximum pressure (in Pascals) that the block can exert on the surface? $\left(g = 10\,\dfrac{\text{N}}{\text{kg}}\right)$
(1) $1.6 \times 10^3$ (2) $4 \times 10^3$ (3) $1.6 \times 10^4$ (4) $4 \times 10^4$

192. In the figure below, the temperature of the gas is 27 degrees Celsius and the mercury level is 75 cm. If we increase the temperature of the gas to 30 degrees Celsius, how many centimeters of mercury should we add to branch A so that the mercury level in branch M remains the same (i.e., stays at surface M)?
[Figure: A U-tube manometer with a gas flask connected on the left side, mercury at the bottom, and branch A on the right side. Points M and M' are marked on the mercury surface.]

• [(1)] 25
• [(2)] 15
• [(3)] 7.5
• [(4)] 5.5

193. A uniform rod of length $L$ is connected between two sources at temperatures $100\,^\circ\text{C}$ and $0\,^\circ\text{C}$. What fraction $L_1$ of $L$ from the left end should point M be located so that the temperature at point M is 30 degrees Celsius? (Heat exchange between the rod's surface and the environment is neglected.)
[Figure: A uniform rod of length $L$ with the left end at $100\,^\circ\text{C}$ and the right end at $0\,^\circ\text{C}$. Point M is located at distance $L_1$ from the left end.]

• [(1)] 0.3
• [(2)] 0.5
• [(3)] 0.7
• [(4)] 0.75

194. An air bubble with volume $1.40\,\text{cm}^3$ rises from the bottom of a lake where the pressure is $1.8 \times 10^5\,\text{Pa}$ and the temperature is 7 degrees Celsius, to the surface of the lake where the temperature is 27 degrees Celsius and the pressure is $1.0 \times 10^5\,\text{Pa}$. During this process, how many cubic centimeters does the volume of the bubble change?
(1) $1.30$ (2) $1.28$ (3) $1.07$ (4) $0.70$
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195. In an isobaric process, if the volume of gas changes from $5\,\text{Lit}$ to $4\,\text{Lit}$, the work done on the gas equals $W_1$ and the change in internal energy of gas $\Delta U_1$. If in the continuation of the same process, the volume of gas changes from $4\,\text{Lit}$ to $3\,\text{Lit}$, the work done on the gas equals $W_2$ and the change in internal energy of gas $\Delta U_2$. Which of the following relations is correct?
\begin{align*} &(1) \Delta U_2 = \Delta U_1 \ , W_2 = W_1 (2) \Delta U_2 > \Delta U_1 \ , W_2 > W_1 &(3) \Delta U_1 > \Delta U_2 \ , W_1 > W_2 (4) \Delta U_2 > \Delta U_1 \ , W_1 > W_2 \end{align*}

196. In a refrigerator, heat that is expelled to the outside is $\dfrac{5}{4}$ of the heat absorbed from inside the refrigerator. What is the coefficient of performance of this refrigerator?
\[ (1)\quad 2 \qquad (2)\quad 3 \qquad (3)\quad 4 \qquad (4)\quad 5 \]

197. The $(P-V)$ diagram of a certain ideal gas is shown below. The internal energy of the gas at state $c$ is how many joules more than at state $a$? $\left(C_P = \dfrac{5}{2}R\right)$
[Figure: P-V diagram with pressure axis P(Pa) and volume axis V(lit). Points a and b are connected by a dashed horizontal line at pressure $10^5$ Pa. Points b and c are connected by a dashed vertical line. Point c is at volume 8 lit and pressure $10^5$ Pa. The process from a to b is isobaric (isothermal label shown), and from b to c is isochoric. The volume axis shows values 2, 5, 8 and pressure axis shows $10^5$.]
\begin{align*} &(1) 450 &(2) 720 &(3) 750 &(4) 1500 \end{align*}