35. The phase space diagram for a ball thrown vertically up from ground is (A) [Figure] (B) [Figure] (C) [Figure] (D) [Figure]
ANSWER: D
The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $\mathrm { E } _ { 1 }$ and $\mathrm { E } _ { 2 }$ are the total mechanical energies respectively. Then (A) $\quad E _ { 1 } = \sqrt { 2 } E _ { 2 }$ (B) $E _ { 1 } = 2 E _ { 2 }$ (C) $E _ { 1 } = 4 E _ { 2 }$ (D) $E _ { 1 } = 16 E _ { 2 }$ [Figure]
ANSWER: C
Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is (A) [Figure] (B) [Figure] (C) [Figure] (D) [Figure]
ANSWER: B
Paragraph for Question Nos. 38 and 39
A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let ' $N$ ' be the number density of free electrons, each of mass ' $m$ '. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. If the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency ' $\omega _ { \mathrm { p } }$ ', which is called the plasma frequency. To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency $\omega$, where a part of the energy is absorbed and a part of it is reflected. As $\omega$ approaches $\omega _ { \mathrm { p } }$, all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.
Taking the electronic charge as ˋeˋ and the permittivity as ˋ $\varepsilon _ { \mathrm { O } }$ ˋ use dimensional analysis to determine the correct expression for $\omega p$
35. The phase space diagram for a ball thrown vertically up from ground is\\
(A)\\
\includegraphics[max width=\textwidth, alt={}, center]{cdfce4af-7f3d-4d66-ab09-7da7ecb927ff-16_451_490_367_369}\\
(B)\\
\includegraphics[max width=\textwidth, alt={}, center]{cdfce4af-7f3d-4d66-ab09-7da7ecb927ff-16_504_565_380_1132}\\
(C)\\
\includegraphics[max width=\textwidth, alt={}, center]{cdfce4af-7f3d-4d66-ab09-7da7ecb927ff-16_517_413_965_371}\\
(D)\\
\includegraphics[max width=\textwidth, alt={}, center]{cdfce4af-7f3d-4d66-ab09-7da7ecb927ff-16_536_492_928_1135}
\section*{ANSWER: D}
\begin{enumerate}
\setcounter{enumi}{35}
\item The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and $\mathrm { E } _ { 1 }$ and $\mathrm { E } _ { 2 }$ are the total mechanical energies respectively. Then\\
(A) $\quad E _ { 1 } = \sqrt { 2 } E _ { 2 }$\\
(B) $E _ { 1 } = 2 E _ { 2 }$\\
(C) $E _ { 1 } = 4 E _ { 2 }$\\
(D) $E _ { 1 } = 16 E _ { 2 }$\\
\includegraphics[max width=\textwidth, alt={}, center]{cdfce4af-7f3d-4d66-ab09-7da7ecb927ff-17_670_728_253_1164}
\end{enumerate}
\section*{ANSWER: C}
\begin{enumerate}
\setcounter{enumi}{36}
\item Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is\\
(A)\\
\includegraphics[max width=\textwidth, alt={}, center]{cdfce4af-7f3d-4d66-ab09-7da7ecb927ff-17_388_470_1359_344}\\
(B)\\
\includegraphics[max width=\textwidth, alt={}, center]{cdfce4af-7f3d-4d66-ab09-7da7ecb927ff-17_398_489_1349_981}\\
(C)\\
\includegraphics[max width=\textwidth, alt={}, center]{cdfce4af-7f3d-4d66-ab09-7da7ecb927ff-17_366_459_1785_364}\\
(D)\\
\includegraphics[max width=\textwidth, alt={}, center]{cdfce4af-7f3d-4d66-ab09-7da7ecb927ff-17_391_490_1760_994}
\end{enumerate}
ANSWER: B
\section*{Paragraph for Question Nos. 38 and 39}
A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let ' $N$ ' be the number density of free electrons, each of mass ' $m$ '. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. If the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency ' $\omega _ { \mathrm { p } }$ ', which is called the plasma frequency. To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency $\omega$, where a part of the energy is absorbed and a part of it is reflected. As $\omega$ approaches $\omega _ { \mathrm { p } }$, all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.\\