PhysicsBowl 2018
Instruction
- Questions: The test is composed of 50 questions; however, students answer only 40 questions.
Division 1 students will answer only questions 1 – 40. Do not answer questions 41 – 50.
Division 2 students will answer only questions 11 – 50. Do not answer questions 1 – 10. - Calculator: A hand-held calculator may be used. Any memory must be cleared of data and programs. Calculators may not be shared.
- Formulas and constants: Only the formulas and constants provided with the contest may be used.
- Time limit: 45 minutes.
- Treat g = 10 m/s$^2$ for all questions
A quick Google search reveals that your phone operates at a frequency of $850\times10^6$ Hz. Which of the following choices best represents this frequency using metric prefixes?
$\textbf{(A) }$ 850 $\mu$Hz$ \qquad$ $\textbf{(B) }$ 850 mHz$ \qquad$ $\textbf{(C) }$ 850 kHz$ \qquad$ $\textbf{(D) }$ 850 MHz$ \qquad$ $\textbf{(E) }$ 850 GHz
$\textbf{D}$
Mega (M) is $10^6$... What about MAGA 🙂
A standard metal electroscope is positively charged. A person that is grounded (neutral charge) then touches the top portion of the electroscope with finger. Which one of the following choices most correctly explains what happens when the finger touches the electroscope?
$\textbf{(A) }$ The leaves of the electroscope come back together because excess protons conduct to the finger from the electroscope.$\newline$
$\textbf{(B) }$ The leaves of the electroscope come back together because electrons conduct to the electroscope from the finger.$\newline$
$\textbf{(C) }$ The leaves remain where they are as nothing occurs.$ \newline$
$\textbf{(D) }$ The leaves of the electroscope move apart as electrons conduct from the electroscope to the finger.$ \newline$
$\textbf{(E) }$ The leaves of the electroscope move apart as protons conduct from the finger to the electroscope.
$\textbf{B}$
Leaves turn to neutral due to electrons from finger.
Which of the following is $\textit{NOT}$ a vector quantity?
$\textbf{(A) }$ Acceleration$ \qquad\newline$ $\textbf{(B) }$ Average velocity $ \qquad\newline$ $\textbf{(C) }$ Linear momentum$ \qquad\newline$ $\textbf{(D) }$ Potential energy$ \qquad\newline$ $\textbf{(E) }$ Force
$\textbf{D}$
A vector has both direction and magnitude.
A ball is thrown vertically downward with an initial speed of 12.0 m/s from a height of 10.0 m above the ground. Ignoring air resistance, what is the speed of the ball when it reaches the ground?
$\textbf{(A) }$ 18.5 m/s$ \qquad$ $\textbf{(B) }$ 14.6 m/s$ \qquad$ $\textbf{(C) }$ 14.0 m/s$ \qquad$ $\textbf{(D) }$ 12.8 m/s$ \qquad$ $\textbf{(E) }$ 12.0 m/s
$\textbf{A}$
$v^2=v_0^2+2gh$
A particle travels at a constant speed around a circular path of radius $R$. If the particle makes one complete trip around the entire circle, what is the magnitude of the displacement for this trip?
$\textbf{(A) }$ $\pi R \qquad$ $\textbf{(B) }$ $2R \qquad$ $\textbf{(C) }$ $2\pi R \qquad$ $\textbf{(D) }$ $4R \qquad$ $\textbf{(E) }$ 0
$\textbf{E}$
The displacement is a vector.
What temperature on the Kelvin scale is equivalent to $37^\circ$C?
$\textbf{(A) }$ 310 K$ \qquad$ $\textbf{(B) }$ 283 K$ \qquad$ $\textbf{(C) }$ 256 K$ \qquad$ $\textbf{(D) }$ 37 K$ \qquad$ $\textbf{(E) }$ 19 K
$\textbf{A}$
The formula between temperature in Kelvin $T$ and in Celsius $t$ is $T=t+273$.
What is the percent uncertainty in the measurement $2.54\pm0.16$ cm?
$\textbf{(A) }$ $2.9\% \qquad$ $\textbf{(B) }$ $6.3\% \qquad$ $\textbf{(C) }$ $8.7\% \qquad$ $\textbf{(D) }$ $12.6\% \qquad$ $\textbf{(E) }$ $14\%$
$\textbf{B}$
$0.16/2.54=6.3\%$
An Olympic bobsled needs to negotiate a 100 m radius turn at 35 m/s without skidding. What minimum banking angle of the turn is needed for this to happen? (Ignore friction)
$\textbf{(A) }$ $21^\circ \qquad$ $\textbf{(B) }$ $31^\circ \qquad$ $\textbf{(C) }$ $41^\circ \qquad$ $\textbf{(D) }$ $51^\circ \qquad$ $\textbf{(E) }$ $61^\circ$
$\textbf{D}$
The horizontal component of the normal force provides the centripetal force, thus $mg\tan\theta=m\dfrac{v^2}{R}$, so $\theta=\arctan\dfrac{v^2}{gR}$.
The mean diameter of the Earth is $12.76\times10^3$ km. What is the surface area of the Earth in m$^2$?
$\textbf{(A) }$ $4.01\times10^7 \qquad\newline$ $\textbf{(B) }$ $5.12\times10^{14} \qquad\newline$ $\textbf{(C) }$ $1.09\times10^{21} \qquad\newline$ $\textbf{(D) }$ $1.68\times10^9 \qquad\newline$ $\textbf{(E) }$ $2.05\times10^{15}$
$\textbf{B}$
The surface area $A=4\pi r^2$.
A 2.0 m long organ pipe which is open at both ends resonates at its fundamental frequency. Neglecting any end effects, what wavelength is formed by this pipe in this mode of vibration?
$\textbf{(A) }$ 1 meter$ \qquad$ $\textbf{(B) }$ 2 meters$ \qquad$ $\textbf{(C) }$ 4 meters$ \qquad$ $\textbf{(D) }$ 6 meters$ \qquad$ $\textbf{(E) }$ 8 meters
$\textbf{C}$
For an open pipe, the length $L=\dfrac{\lambda}2$.
In a classroom demonstration, a teacher discussing the air in the room as an ideal gas slides a solid barrier of negligible thickness into place, cutting the room into two equal-sized volumes. What is the air pressure
for the portion of the room in which the teacher is standing, assuming the original pressure in the whole room was $P$? Treat the room as a sealed container.
$\textbf{(A) }$ $\dfrac14P \qquad$ $\textbf{(B) }$ $\dfrac12P \qquad$ $\textbf{(C) }$ $P \qquad$ $\textbf{(D) }$ $2P \qquad$ $\textbf{(E) }$ $4P$
$\textbf{C}$
The pressure is uniform in the room.
What is the equivalent resistance in the circuit that is shown below?
$\textbf{(A) }$ $55\ \Omega \qquad$ $\textbf{(B) }$ $80\ \Omega \qquad$ $\textbf{(C) }$ $50\ \Omega \qquad$ $\textbf{(D) }$ $45\ \Omega \qquad$ $\textbf{(E) }$ $75\ \Omega$
$\textbf{C}$
$R_2$ and $R_3$ are in parallel, so $R_{23}=10\ \Omega$, then $R=R_1+R_{23}+R_4=50\ \Omega$.
An x-ray photon collides with a free electron, and the photon is scattered. During the collision:
$\textbf{(A) }$ there is conservation of momentum but not energy$ \qquad\newline$
$\textbf{(B) }$ there is conservation of neither momentum nor energy$ \qquad\newline$
$\textbf{(C) }$ there is conservation of energy but not momentum$ \qquad\newline$
$\textbf{(D) }$ there is conservation of both momentum and energy$ \qquad\newline$
$\textbf{(E) }$ impossible to predict if momentum and energy are conserved without additional information
$\textbf{D}$
Both momentum and energy are conserved.
Three identical wood blocks are raced across three different flat surfaces, with the faces of the blocks on the surfaces. Each block is pulled horizontally with the same force $F$ from one edge by a light string attached to the block. Block 1 is pulled on a frictionless surface. Block 2 is pulled on a surface with a nonzero kinetic friction coefficient, and a zero static friction coefficient. Block 3 is pulled on a surface with a nonzero static friction coefficient, and the same kinetic coefficient as for Block 2, where $\mu_k<\mu_s$. If each block starts from rest and is pulled until traveling the same fixed horizontal distance, which of the following choices correctly ranks the times ($t_1$, $t_2$, $t_3$) it takes for each block to traverse the distance?
$\textbf{(A) }$ $t_1<t_2<t_3 \qquad\newline$ $\textbf{(B) }$ $t_1=t_2=t_3 \qquad\newline$ $\textbf{(C) }$ $t_1<t_2=t_3 \qquad\newline$ $\textbf{(D) }$ $t_3<t_2<t_1 \qquad\newline$ $\textbf{(E) }$ $t_2<t_3<t_1$
$\textbf{C}$
Block 1 will experience no friction and will therefore travel the distance in the least amount of time. Blocks 2 and 3 will experience equivalent amounts of kinetic friction force and will take equal amounts of time to travel.
A sample of ideal gas is in a container at a temperature of $100\ ^\circ \text{C}$ and a pressure of 2.5 atm. If the volume of the container is 0.025 m$^3$, approximately how many molecules of gas are in the container?
$\textbf{(A) }$ $4.58\times10^{24} \qquad\newline$ $\textbf{(B) }$ $1.23\times10^{24} \qquad\newline$ $\textbf{(C) }$ $6.25\times10^{23} \qquad\newline$ $\textbf{(D) }$ $4.53\times10^{22} \qquad\newline$ $\textbf{(E) }$ $1.21\times10^{22}$
$\textbf{B}$
The mole number of molecules is $n=\dfrac{PV}{RT}$, so the number of molecules is $N=nN_A$.
Determining the area under an object’s acceleration vs. time graph for a fixed time interval will calculate
$\textbf{(A) }$ the object’s average velocity during the time interval$ \qquad\newline$
$\textbf{(B) }$ the object’s velocity at the end of the time interval$ \qquad\newline$
$\textbf{(C) }$ the object’s average speed during the time interval$ \qquad\newline$
$\textbf{(D) }$ the object’s change in velocity during the time interval$ \qquad\newline$
$\textbf{(E) }$ the object’s velocity at the time midway through the time interval
$\textbf{D}$
$\Delta v=\int a\ \text{d}t$
A thick-walled metal pipe of length 20.0 cm has an inside diameter of 2.00 cm and an outside diameter of 2.40 cm. What is the total surface area of the pipe, including the inside, outside, and ends, in cm$^2$?
$\textbf{(A) }$ 276$ \qquad$ $\textbf{(B) }$ 277$ \qquad$ $\textbf{(C) }$ 278$ \qquad$ $\textbf{(D) }$ 279$ \qquad$ $\textbf{(E) }$ 282
$\textbf{D}$
The inside surface area $A_1=\pi d_1\cdot l$;$\newline$
The outside surface area $A_2=\pi d_2\cdot l$;$\newline$
The ends area $A_3=2\pi(r_2^2-r_1^2)$;$\newline$
The total surface area $A=A_1+A_2+A_3$.
The circuit shown contains a battery with an internal resistance, $r$ connected to a variable resistor. When the resistance of the variable resistor is increased, which of the following statements is true?
$\textbf{(A) }$ The terminal voltage increases.$ \qquad\newline$
$\textbf{(B) }$ The current through the variable resistor in the circuit increases.$ \qquad\newline$
$\textbf{(C) }$ The power dissipated by the internal resistance increases.$ \qquad\newline$
$\textbf{(D) }$ The potential difference across the variable resistor decreases.$ \qquad\newline$
$\textbf{(E) }$ None of the above statements are true.
$\textbf{A}$
The current $I=\dfrac{U}{r+R}$ decreased when the variable resistor $R$ increased, so the internal voltage decreased and the terminal voltage increased.
Which of the following $\textit{could}$ produce an enlarged but inverted image of a real object?
$\textbf{(A) }$ A converging lens placed at a distance greater than its focal length from the object.$ \qquad\newline$
$\textbf{(B) }$ A converging lens placed at a distance less than its focal length from the object.$ \qquad\newline$
$\textbf{(C) }$ A diverging lens placed at a distance less than the magnitude of its focal length from the object.$ \qquad\newline$
$\textbf{(D) }$ A diverging lens placed at a distance greater than the magnitude of its focal length from the object.$ \qquad\newline$
$\textbf{(E) }$ It is not possible to create the type of image desired.
$\textbf{A}$
An enlarged and inverted image means the magnification $M=-\dfrac{d_i}{d_o}<-1$. $\newline$
According to $\dfrac1{d_o}+\dfrac1{d_i}=\dfrac1f$, we get $f<d_o<2f$.
A frictionless, solid disk pulley has a mass of 7.07 kg, a radius of 66.0 cm, and is free to rotate vertically about an axle. A rope is wrapped around the disk, a 1.53 kg mass is attached to the end of the rope, and the mass is allowed to fall vertically. What is the angular acceleration of the pulley?
$\textbf{(A) }$ 4.58 rad/s$^2 \qquad$ $\textbf{(B) }$ 7.98 rad/s$^2 \qquad$ $\textbf{(C) }$ 9.87 rad/s$^2 \qquad$ $\textbf{(D) }$ 2.25 rad/s$^2 \qquad$ $\textbf{(E) }$ zero
$\textbf{A}$
Assuming the tension in the rope is $T$. $\newline$
For mass $m=1.53\ \text{kg}$, we have $mg-T=ma$. $\newline$
For the disk pulley, $Tr=I\beta$, where the moment of inertia $I=\dfrac12Mr^2$ and angular acceleration $\beta=\dfrac{a}{r}$, so we get $\beta=\dfrac{mg}{(\frac12M+m)r}$.
Questions 21 and 22 relate to the following information:
A small object is released from rest and reaches the ground in a time of 2.50 s. Neglect air resistance.
With what speed does the object reach the ground?
$\textbf{(A) }$ 31.3 m/s$ \qquad$ $\textbf{(B) }$ 25.0 m/s$ \qquad$ $\textbf{(C) }$ 12.5 m/s$ \qquad$ $\textbf{(D) }$ 10.0 m/s$ \qquad$ $\textbf{(E) }$ 2.5 m/s
$\textbf{B}$
$v=gt$
From what height above the ground was the object released?
$\textbf{(A) }$ 6.25 m$ \qquad$ $\textbf{(B) }$ 12.5 m$ \qquad$ $\textbf{(C) }$ 25.0 m$ \qquad$ $\textbf{(D) }$ 31.3 m$ \qquad$ $\textbf{(E) }$ 62.5 m
$\textbf{D}$
$h=\dfrac{v^2}{2g}$
Induced electric currents due to changing magnetic flux can be explained using which one of the following laws?
$\textbf{(A) }$ Gauss’s Law$ \qquad\newline$ $\textbf{(B) }$ Faraday’s Law$ \qquad\newline$ $\textbf{(C) }$ Ohm’s Law$ \qquad\newline$ $\textbf{(D) }$ Ampere’s Law$ \qquad\newline$ $\textbf{(E) }$ Volta’s Law
$\textbf{B}$
Faraday is your best friend 🙂
A small ball is thrown at an angle of 30.0$^\circ$ above the horizontal ground with a speed of 20.0 m/s. What is the maximum height above the launch point to which the ball rises? Ignore air resistance.
$\textbf{(A) }$ 2.5 m$ \qquad$ $\textbf{(B) }$ 5.0 m$ \qquad$ $\textbf{(C) }$ 10.0 m$ \qquad$ $\textbf{(D) }$ 15.0 m$ \qquad$ $\textbf{(E) }$ 20.0 m
$\textbf{B}$
The vertical component of the velocity is $v_\perp=v\sin\theta$, so the height the ball can reach is $h=\dfrac{v_\perp^2}{2g}$.
In a circuit, the flow of electrons in a horizontal wire produces a constant current of 3.20 A for a time of 3.0 hours. Which of the following choices best represents the number of electrons that pass through a vertical cross-section of wire during this time?
$\textbf{(A) }$ 9.6 $ \qquad\newline$
$\textbf{(B) }$ $6.00\times10^{19} \qquad\newline$
$\textbf{(C) }$ $7.20\times10^{22}\qquad\newline$
$\textbf{(D) }$ $2.16\times10^{23} \qquad\newline$
$\textbf{(E) }$ $6.02\times10^{23}$
$\textbf{D}$
The total charge passing through the cross-section is $Q=It=3.456\times10^4\ \text{C}$.$\newline$
For each electron $e=1.6\times10^{-19}\ \text{C}$, the number of electrons passing through is $n=Q/e$.
A simple pendulum consists of a mass $M$ attached to a string of length $L$ of negligible mass. For this system, when undergoing small oscillations
$\textbf{(A) }$ the frequency is proportional to the amplitude.$ \qquad\newline$
$\textbf{(B) }$ the period is proportional to the amplitude.$ \qquad\newline$
$\textbf{(C) }$ the frequency is independent of the mass $M$.$ \qquad\newline$
$\textbf{(D) }$ the frequency is independent of the length L.$ \qquad\newline$
$\textbf{(E) }$ the frequency is inversely proportional to the length $L$.
$\textbf{C}$
The period $T=2\pi\sqrt{\dfrac{L}{g}}$, the frequency $f=\dfrac1T$, so $f$ is independent of the mass $M$.
Electrons flow from right to left in a wire. A proton is directly above the wire and moving upward as shown. What is the direction of the magnetic force on the proton?
$\textbf{(A) }$ to the left$ \qquad\newline$
$\textbf{(B) }$ to the right$ \qquad\newline$
$\textbf{(C) }$ into the plane of the page$ \qquad\newline$
$\textbf{(D) }$ out of the plane of the page$ \qquad\newline$
$\textbf{(E) }$ toward the wire
$\textbf{B}$
Electrons are negatively charged and flowed from right to left, so the current is in the opposite direction, the magnetic field at the point of the proton is out of the plane, and force on the positively charged proton is to the right.
At the top of a high cliff, a small rock is dropped from rest. A ball is launched straight downward with an initial speed of 36.0 m/s at a time of 2.10 s after the rock was dropped from the same cliff. When the ball has fallen 28.0 m further than the initially dropped rock, what is the speed of the ball relative to the rock?
$\textbf{(A) }$ 15.0 m/s$ \qquad$ $\textbf{(B) }$ 16.0 m/s$ \qquad$ $\textbf{(C) }$ 20.0 m/s$ \qquad$ $\textbf{(D) }$ 21.0 m/s$ \qquad$ $\textbf{(E) }$ 36.0 m/s
$\textbf{A}$
At $t=2.10$ s after the rock dropped, the speed of rock is $v=gt=21\ \text{m/s}$, the relative speed between the ball and the rock is 15 m/s. The relative speed will not change before hitting the ground because both the ball and rock are accelerated by the same gravity.
An object that is 8.60 cm tall is placed in front of a convex mirror. The resulting image is 7.60 cm tall, and 14.2 cm from the mirror. What is the focal length of the mirror?
$\textbf{(A) }$ -122 cm$ \qquad$ $\textbf{(B) }$ -105 cm$ \qquad$ $\textbf{(C) }$ 14.0 cm$ \qquad$ $\textbf{(D) }$ -16.9 cm$ \qquad$ $\textbf{(E) }$ -4.2 cm
$\textbf{A}$
The magnification $M=\dfrac{h_i}{h_o}=-\dfrac{d_i}{d_o}$, so $d_o=-\dfrac{h_o}{h_i}d_i$. Actually the object distance can't be negative because the object is placed in front of the convex mirror, so the height of image must be $h_i=-7.6\ \text{cm}$. The focal length $$f=\dfrac{d_od_i}{d_o+d_i}=-122\ \text{cm}$$
A radian per second is a unit of:
$\textbf{(A) }$ angular displacement$ \qquad\newline$
$\textbf{(B) }$ angular velocity$ \qquad\newline$
$\textbf{(C) }$ angular acceleration$ \qquad\newline$
$\textbf{(D) }$ angular momentum$ \qquad\newline$
$\textbf{(E) }$ rotational kinetic energy
$\textbf{B}$
rad/s is the unit of angular velocity.
A standing transverse wave is formed on a tightly stretched string. The distance between a node and an adjacent antinode is:
$\textbf{(A) }$ 1/8 wavelength$ \qquad\newline$
$\textbf{(B) }$ 1/4 wavelength$ \qquad\newline$
$\textbf{(C) }$ 1/2 wavelength$ \qquad\newline$
$\textbf{(D) }$ 1 wavelength$ \qquad\newline$
$\textbf{(E) }$ unable to be determined without more information
$\textbf{B}$
The distance between a node and an adjacent antinode is $\dfrac14\lambda$.
For a negative point charge, the electric field vectors:
$\textbf{(A) }$ circle the charge$ \qquad\newline$
$\textbf{(B) }$ point radially in toward the charge$ \qquad\newline$
$\textbf{(C) }$ point radially away from the charge$ \qquad\newline$
$\textbf{(D) }$ pass directly through the charge$ \qquad\newline$
$\textbf{(E) }$ cross at infinity
$\textbf{B}$
Onde a terra acaba e o mar começa...$\newline$
Where the land ends and the sea begins...$\newline$
陆止于此海始于斯...
A torque of 150 Newton-meters causes the driveshaft of a car to rotate at 450 radians per second. How much power is produced by this torque?
$\textbf{(A) }$ 53,300 W$ \qquad$ $\textbf{(B) }$ 67,000 W$ \qquad$ $\textbf{(C) }$ 70,000 W$ \qquad$ $\textbf{(D) }$ 72,500 W$ \qquad$ $\textbf{(E) }$ 75,000 W
$\textbf{B}$
$P=\vec{F}\cdot\vec{v}=\vec{F}\cdot(\vec\omega\times\vec{r})=(\vec{r}\times\vec{F})\cdot\vec\omega=\vec\tau\cdot\vec\omega$
For the hydrogen atom, which series describes electron transitions to the N=1 orbit, the lowest energy electron orbit?
$\textbf{(A) }$ Lyman series$ \qquad\newline$ $\textbf{(B) }$ Balmer series$ \qquad\newline$ $\textbf{(C) }$ Paschen series$ \qquad\newline$ $\textbf{(D) }$ Curie series$ \qquad\newline$ $\textbf{(E) }$ Bohr series
$\textbf{A}$
Lowest energy transitions are Lyman series.
200 turns of wire are wrapped on a square frame with sides 18 cm. A uniform magnetic field is applied perpendicular to the plane of the coil. If the field changes uniformly from 0.50 T to 0 in 8.0 s, find the average value of the induced $\textit{emf}$.
$\textbf{(A) }$ 2.05 V$ \qquad$ $\textbf{(B) }$ 4.05 V$ \qquad$ $\textbf{(C) }$ 0.205 V$ \qquad$ $\textbf{(D) }$ 0.405 V$ \qquad$ $\textbf{(E) }$ 0.605 V
$\textbf{D}$
$\mathcal{E}=N\dfrac{\Delta\phi}{\Delta t}=NS\dfrac{\Delta B}{\Delta t}$
A 0.30 kg mass is suspended on a vertical spring. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. What is the period of oscillation?
$\textbf{(A) }$ 0.14 s$ \qquad$ $\textbf{(B) }$ 0.28 s$ \qquad$ $\textbf{(C) }$ 0.024 s$ \qquad$ $\textbf{(D) }$ 0.046 s$ \qquad$ $\textbf{(E) }$ 0.064 s
$\textbf{B}$
The period $T=2\pi\sqrt{\dfrac{m}{k}}$, where $\dfrac{m}{k}$ can be find in $mg=kx$.
An electron is traveling due north and has a speed of $4.0\times10^5\ \text{m/s}$. It enters a region where the Earth's magnetic field has the magnitude $5.0\times10^{-5}\ \text{T}$ to the north and directed downward at $45^\circ$ below the horizontal. What is the magnitude of the force acting on the electron?
$\textbf{(A) }$ $2.3\times10^{-18}\ \text{N} \qquad\newline$ $\textbf{(B) }$ $3.2\times10^{-18}\ \text{N} \qquad\newline$ $\textbf{(C) }$ $4.2\times10^{-18}\ \text{N} \qquad\newline$ $\textbf{(D) }$ $2.5\times10^{-19}\ \text{N} \qquad\newline$ $\textbf{(E) }$ $3.23\times10^{-19}\ \text{N}$
$\textbf{A}$
$F=qvb\sin\theta$
Why does the sky appear to be more blue when looking directly overhead than it does when looking toward the horizon?
$\textbf{(A) }$ The atmosphere is denser at higher altitude than it is at the Earth's surface.$ \qquad\newline$
$\textbf{(B) }$ The temperature of the upper atmosphere is higher than it is at the Earth's surface.$ \qquad\newline$
$\textbf{(C) }$ There are fewer clouds directly overhead than near the horizon.$ \qquad\newline$
$\textbf{(D) }$ The sunlight travels over a longer path at the horizon, resulting in more scattering.$ \qquad\newline$
$\textbf{(E) }$ The sunlight entering the atmosphere from directly above undergoes greater refraction and dispersion.
$\textbf{D}$
Detailed explanation can be found in wiki: Rayleigh scattering.
A mass that is in simple harmonic motion obeys the following position versus time equation: $y=(0.50\ \text{m})\sin(\dfrac\pi2t)$ where $t$ is in seconds. What is the period of vibration of this mass?
$\textbf{(A) }$ 1.0 s$ \qquad$ $\textbf{(B) }$ 2.0 s$ \qquad$ $\textbf{(C) }$ 3.0 s$ \qquad$ $\textbf{(D) }$ 4.0 s$ \qquad$ $\textbf{(E) }$ 5.0 s
$\textbf{D}$
The period $T=2\pi\div\dfrac\pi2=4\ \text{s}$.
Which of the following wavelengths (in nm) of electromagnetic radiation will produce photoelectrons of the least kinetic energy if the radiation is incident on a material with a work function of $4.80\ \text{eV}$?
$\textbf{(A) }$ 992$ \qquad$ $\textbf{(B) }$ 496$ \qquad$ $\textbf{(C) }$ 248$ \qquad$ $\textbf{(D) }$ 124$ \qquad$ $\textbf{(E) }$ 62
$\textbf{C}$
For $h\nu=h\dfrac{c}{\lambda}=W$, the wavelength $\lambda=\dfrac{hc}{W}=259\ \text{nm}$. Any wavelength shorter than 259 nm can produce photoelectrons.
An object of mass $m$ is initially at rest. After this object is accelerated to a speed of $2.40\times10^8\ \text{m/s}$, it collides with and sticks to a second object of mass $m$ that is at rest. Immediately after the collision, what is the common speed of the two masses?
$\textbf{(A) }$ $2.25\times10^8\ \text{m/s} \qquad\newline$ $\textbf{(B) }$ $1.80\times10^8\ \text{m/s} \qquad\newline$ $\textbf{(C) }$ $1.66\times10^8\ \text{m/s} \qquad\newline$ $\textbf{(D) }$ $1.50\times10^8\ \text{m/s} \qquad\newline$ $\textbf{(E) }$ $1.20\times10^8\ \text{m/s}$
$\textbf{C}$
The speed of the first object is $v_0=0.8c$. Assuming the common speed after collision is $v$, the linear momentum is conserved in the collision process, so we have $$\dfrac{m}{\sqrt{1-v_0^2/c^2}}v_0=\dfrac{2m}{\sqrt{1-v^2/c^2}}v$$ By solving the equation we get $v=\dfrac2{\sqrt{13}}c$.
Two moles of an ideal gas absorbs 2100 J of heat during an isobaric process. If the gas changes temperature by $36^\circ\text{C}$ during the process, which one of the following choices could identify the gas?
$\textbf{(A) }$ Carbon monoxide $ \qquad\newline$ $\textbf{(B) }$ Water vapor$ \qquad\newline$ $\textbf{(C) }$ Ammonia$ \qquad\newline$ $\textbf{(D) }$ Helium$ \qquad\newline$ $\textbf{(E) }$ Hydrogen sulfide
$\textbf{A}$
For an isobaric process, $Q=W+\Delta U=p\Delta V+\dfrac{i}{2}nR\Delta T=\dfrac{i+2}{2}nR\Delta T$. By solving the equation we get $i=5$, which means the gas is made up of diatomic molecules.
In August of 2017, the gravitational waves from the collision and merger of two neutron stars were detected. After their collision, several forms of electromagnetic radiation were subsequently detected. What was the first type of electromagnetic radiation detected after the gravitational waves were detected?
$\textbf{(A) }$ Gamma rays$ \qquad\newline$ $\textbf{(B) }$ Visible light$ \qquad\newline$ $\textbf{(C) }$ Radio waves$ \qquad\newline$ $\textbf{(D) }$ X-rays$ \qquad\newline$ $\textbf{(E) }$ Microwaves
$\textbf{A}$
Well...now you know it.
Which of the following terms/quantities is most closely associated with “the measure of resistance of an object to length change under lengthwise tension or compression”?
$\textbf{(A) }$ Bulk modulus$ \qquad\newline$ $\textbf{(B) }$ Plastic deformation $ \qquad\newline$ $\textbf{(C) }$ Shear modulus$ \qquad\newline$ $\textbf{(D) }$ Elastic limit $ \qquad\newline$ $\textbf{(E) }$ Young's modulus
$\textbf{E}$
Detailed explanation can be found in wiki: Young's modulus
According to Lenz's law, the direction of an induced current in a conductor will be that which tends to produce which of the following effects?
$\textbf{(A) }$ Enhance the effect which produces it.$ \qquad\newline$
$\textbf{(B) }$ Produce a greater heating effect.$ \qquad\newline$
$\textbf{(C) }$ Oppose the greatest voltage.$ \qquad\newline$
$\textbf{(D) }$ Oppose the effect which produces it.$ \qquad\newline$
$\textbf{(E) }$ Enhance the greatest voltage.
$\textbf{D}$
Lenz's law states the induced current will weaken the reason produce it.
When an ideal gas is taken through an isochoric process,
$\textbf{(A) }$ $\Delta U=0 \qquad\newline$ $\textbf{(B) }$ $W=0 \qquad\newline$ $\textbf{(C) }$ $Q=0 \qquad\newline$ $\textbf{(D) }$ $\Delta U=W \qquad\newline$ $\textbf{(E) }$ none of the above
$\textbf{B}$
In an isochoric process the volume do not change, thus no work has been done.
The existence of the neutrino was proposed to explain
$\textbf{(A) }$ alpha decay$ \qquad$ $\textbf{(B) }$ gamma emission$ \qquad$ $\textbf{(C) }$ beta decay$ \qquad$ $\textbf{(D) }$ fission$ \qquad$ $\textbf{(E) }$ fusion
$\textbf{C}$
Tip: google it.
A series RC circuit has a resistance of 2.00 $\Omega$ and a capacitance of 0.010 F. A student plots the natural log of the current in the circuit as a function of time while the capacitor is charging. Which one of the following choices best represents the numerical value associated with the slope of the resulting line?
$\textbf{(A) }$ 0.02$ \qquad$ $\textbf{(B) }$ -0.02$ \qquad$ $\textbf{(C) }$ 50$ \qquad$ $\textbf{(D) }$ -50$ \qquad$ $\textbf{(E) }$ 0.5
$\textbf{D}$
According to Kirchhoff's voltage law $$RI+\dfrac{Q}{C}=V_0$$ By differentiating both side of the equation we get $$R\dfrac{\text{d}I}{\text{d}t}+\dfrac1CI=0$$ or $$\ln I=-\dfrac{1}{RC}t+C$$ so the slope is $k=-\dfrac{1}{RC}=-50$.
A particle has a total energy of 500 $MeV$ and a linear momentum of 300$\dfrac{MeV}{c}$. What is the mass of the particle?
$\textbf{(A) }$ $800\dfrac{MeV}{c^2} \qquad$ $\textbf{(B) }$ $583\dfrac{MeV}{c^2} \qquad$ $\textbf{(C) }$ $400\dfrac{MeV}{c^2} \qquad$ $\textbf{(D) }$ $267\dfrac{MeV}{c^2} \qquad$ $\textbf{(E) }$ $200\dfrac{MeV}{c^2}$
$\textbf{C}$
According to $E^2=c^2p^2+m_0^2c^4$, the mass $m_0=\sqrt{\dfrac{E^2-c^2p^2}{c^4}}=400\dfrac{MeV}{c^2}$.
Two spheres are heated to the same temperature and allowed to radiate energy to identical surroundings. The spheres have the same emissivity, but one sphere has twice the diameter of the other. If the smaller sphere radiates energy at a rate $P$, at what rate will the larger sphere radiate energy?
$\textbf{(A) }$ $P \qquad$ $\textbf{(B) }$ $2P \qquad$ $\textbf{(C) }$ $4P \qquad$ $\textbf{(D) }$ $8P \qquad$ $\textbf{(E) }$ $16P$
$\textbf{C}$
The radiation power is proportional to the surface area $A$, where $A=4\pi r^2$.