Prove the following
Question: Let $\left[\epsilon_{0}\right]$ denote the dimensional formula of the permittivity of vacuum. If $M=$ mass, $L=$ Length, $\mathrm{T}=$ Time and $\mathrm{A}=$ electric current, then : $\left[\epsilon_{0}\right]=\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{2} \mathrm{~A}\right]$$\left[\epsilon_{0}\right]=\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]$$\left[\epsilon_{0}\right]=\left[\mathrm{M}^{-1} \mathrm{~L}^{2} \mathrm{~T}^{-1} \mathrm{~A}^{-2}\ri...
Read More →A travelling wave represented
Question: A travelling wave represented by $\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}-\mathrm{kx})$ is superimposed on another wave represented by $\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}+\mathrm{kx})$. The resultant is :- A standing wave having nodes at $\mathrm{x}=\left(\mathrm{n}+\frac{1}{2}\right) \frac{\lambda}{2}, \mathrm{n}=0,1,2$A wave travelling along $+x$ directionA wave travelling along $-x$ directionA standing wave having nodes at $\mathrm{x}=\frac{\mathrm{n} \lambda}{2} ; ...
Read More →If the series limit frequency of the Lyman series is
Question: If the series limit frequency of the Lyman series is $\mathrm{v}_{\mathrm{L}}$, then the series limit frequency of the Pfund series is :(A) $16 \mathrm{v}_{\mathrm{L}}$$v_{L} / 16$$v_{\mathrm{L}} / 25$$25 \mathrm{v}_{\mathrm{L}}$Correct Option: , 3 Solution:...
Read More →In a uniformly charged sphere of total charge Q and radius R,
Question: In a uniformly charged sphere of total charge $\mathrm{Q}$ and radius $\mathrm{R}$, the electric field $\mathrm{E}$ is plotted as a function of distance from the centre. The graph which would correspond to the above will be :-Correct Option: , 4 Solution:...
Read More →An electron from various excited states of hydrogen atom emit radiation
Question: An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let $\lambda_{\mathrm{n}}, \lambda_{\mathrm{g}}$ be the de Broglie wavelength of the electron in the $\mathrm{n}^{\text {th }}$ state and the ground state respectively. Let $\Lambda_{n}$ be the wavelength of the emitted photon in the transition from the $n^{\text {th }}$ state to the ground state. For large $n,(A, B$ are constants)$\Lambda_{n} \approx \mathrm{A}+\mathrm{B} \lambda_{\mat...
Read More →This question has Statement-1 and Statement-2.
Question: This question has Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. An insulating solid sphere of radius $\mathrm{R}$ has a uniformaly positive charge density $\rho$. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphre and also at a point out side the sphere. The electric potential at infinity is zero. State...
Read More →Solve this following
Question: Statement-1: Two longitudinal waves given by equations : $\mathrm{y}_{1}(\mathrm{x}, \mathrm{t})=2 \mathrm{a} \sin (\omega \mathrm{t}-\mathrm{kx})$ and $\mathrm{y}_{2}(\mathrm{x}, \mathrm{t})=$ a $\sin (2 \omega t-2 k x)$ will have equal intensity. Statement-1: Intensity of waves of given frequency in same medium is proportional to square of amplitude only. Statement- 1 is false, statement- 2 is trueStatement-1 is ture, statement- 2 is falseStatement- 1 is ture, statement- 2 true; stat...
Read More →Two positive charges of magnitude 'q' are placed at the ends of a side (side 1 ) of a square of side '2a'.
Question: Two positive charges of magnitude ' $q$ ' are placed at the ends of a side (side 1 ) of a square of side '2a'. Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge $\mathrm{Q}$ moves from the middle of side 1 to the centre of square, its kinetic energy at the centre of square is :- $\frac{1}{4 \pi \epsilon_{0}} \frac{2 \mathrm{qQ}}{\mathrm{a}}\left(1-\frac{1}{\sqrt{5}}\right)$Zero$\frac{1}{4 \pi \in_{0}} \frac{2 \mathrm{qQ}}{\mathrm{...
Read More →There is a circular tube in
Question: There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_{1}$ and $\mathrm{d}_{2}$ are filled in the tube. Each liquid subtends $90^{\circ}$ angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical. Ratio $\frac{d_{1}}{d_{2}}$ is : $\frac{1+\tan \alpha}{1-\tan \alpha}$$\frac{1+\sin \alpha}{1-\cos \alpha}$$\frac{1+\sin \alpha}{1-\sin \alpha}$$\frac{1+\cos \alpha}{1-\cos \alpha}$Correct Option: 1 Solution:...
Read More →The electrostatic potential inside a charged spherical ball is given by
Question: The electrostatic potential inside a charged spherical ball is given by $\phi=a^{2}+b$ where $r$ is the distance from the centre; $a, b$ are constant. Then the charge density inside the ball is :-$-24 \pi \mathrm{a} \in_{0}$$-6 a \in_{0}$$-24 \pi a \in_{0} r$$-6 a \in_{0} r$Correct Option: , 2 Solution:...
Read More →A particle A of mass m and initial velocity v collides with a particle
Question: A particle A of mass $m$ and initial velocity $v$ collides with a particle $B$ of mass $\frac{m}{2}$ which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $\lambda_{\mathrm{A}}$ to $\lambda_{\mathrm{B}}$ after the collision is :$\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}=\frac{2}{3}$ $\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}=\frac{1}{2}$$\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}=\frac{1}{3}$$\frac{\lambda_{\mathrm{A}}}{...
Read More →The transverse displacement
Question: The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t)=e^{-\left(a x^{2}+b b^{2}+2 \sqrt{a b x}\right)}$. This represents a :- standing wave of frequency $\sqrt{b}$standing wave of frequency $\frac{1}{\sqrt{b}}$wave moving in $+x$ directionwith speed $\sqrt{\frac{a}{b}}$wave moving in $-x$ direction with speed $\sqrt{\frac{b}{a}}$Correct Option: , 4 Solution:...
Read More →Two identical charged spheres suspended from a common point by two massless string of length
Question: Two identical charged spheres suspended from a common point by two massless string of length $\ell$ are initially a distance $\mathrm{d}(\mathrm{d} \ll \ell)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance $x$ between them :-$\mathrm{V} \propto \mathrm{X}^{1 / 2}$$V \propto x$$\mathrm{V} \propto \mathrm{x}^{-1 / 2}$$v \propto x^{-1}...
Read More →Let there be a spherically symmetric charge distribution with charge density varying as
Question: Let there be a spherically symmetric charge distribution with charge density varying as $\rho(r)=\rho_{0}\left(\frac{5}{4}-\frac{r}{R}\right)$ upto $r=R$, and $\rho(r)=0$ for $rR$, where $r$ is the distance from the origin. The electric field at a distance $r(rR)$ from the origion is given by : $\frac{\rho_{0} \mathrm{r}}{3 \varepsilon_{0}}\left(\frac{5}{4}-\frac{\mathrm{r}}{\mathrm{R}}\right)$$\frac{4 \pi \rho_{0} r}{3 \varepsilon_{0}}\left(\frac{5}{3}-\frac{r}{R}\right)$$\frac{\rho_{...
Read More →Some energy levels of a molecule are shown in the figure.
Question: Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $\mathrm{r}=\lambda_{1} / \lambda_{2}$, is given by (A) $r=\frac{3}{4}$$r=\frac{1}{3}$$\mathrm{r}=\frac{4}{3}$$r=\frac{2}{3}$Correct Option: , 2 Solution:...
Read More →On heating water,
Question: On heating water, bubbles being formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius $R$ and making a circular contact of radius $r$ with the bottom of the vessel. If $\mathrm{r} \ll \mathrm{R}$, and the surface tension of water is $\mathrm{T}$, value of $r$ just before bubbles detatch is:(dencity of water is $\rho_{w}$ ) $R^{2} \sqrt{\frac{\rho_{w} g}{T}}$$\mathrm{R}^{2} \sqrt{\frac{3 \rho_{w} \mathrm{~g}}{\mathrm{~T}}}$$\mathrm{R}^{2} \sqrt{\f...
Read More →A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it.
Question: A thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net field $\overrightarrow{\mathrm{E}}$ at the centre $\mathrm{O}$ is :- $\frac{\mathrm{q}}{2 \pi^{2} \varepsilon_{0} \mathrm{r}^{2}} \hat{j}$$\frac{q}{4 \pi^{2} \varepsilon_{0} r^{2}} \hat{j}$$-\frac{\mathrm{q}}{4 \pi^{2} \varepsilon_{0} \mathrm{r}^{2}} \hat{\mathrm{j}}$$-\frac{q}{2 \pi^{2} \varepsilon_{0} r^{2}} \hat{j}$Correct Option: , 4 Solution:...
Read More →Match List-I (Fundament Experiment) with List-II (its conclusion)
Question: Match List-I (Fundament Experiment) with List-II (its conclusion) and select the correct option from the choices given below the list : (A) A-ii, B-i, C-iiiA-iv, B-iii, C-iiA-i, B-iv, C-iiiA-ii, B-iv, C-iiiCorrect Option: 1 Solution: Self Explanatory/Theory (A) Franck-Hertz experiment explains disrete energy levels of atom (B) Photo-electric experiment explain particle nature of light (C) Davison Germer experiment explain wave nature of electron....
Read More →The equation of a wave on a string of linear mass density
Question: The equation of a wave on a string of linear mass density $0.04 \mathrm{~kg} \mathrm{~m}^{-1}$ is given by $\mathrm{y}=0.02(\mathrm{~m}) \sin \left[2 \pi\left(\frac{\mathrm{t}}{0.04(\mathrm{~s})}-\frac{\mathrm{x}}{0.50(\mathrm{~m})}\right)\right]$. The tension in the string is : $6.25 \mathrm{~N}$$4.0 \mathrm{~N}$$12.5 \mathrm{~N}$$0.5 \mathrm{~N}$Correct Option: 1 Solution:...
Read More →Prove the following
Question: Let $\rho(\mathrm{r})=\frac{\mathrm{Q}}{\pi \mathrm{R}^{4}} \mathrm{r}$ be the charge density distribution for a solid sphere of radius $\mathrm{R}$ and total charge $\mathrm{Q}$. For a point 'p' inside the sphere at distance $r_{1}$ from the centre of the sphere, the magnitude of electric field is :- $\frac{\mathrm{Qr}_{1}^{2}}{4 \pi \epsilon_{0} \mathrm{R}^{4}}$$\frac{\mathrm{Qr}_{1}^{2}}{3 \pi \epsilon_{0} \mathrm{R}^{4}}$0$\frac{Q}{4 \pi \epsilon_{0} r_{1}^{2}}$Correct Option: 1 So...
Read More →Two points P and Q are maintained at the potential of
Question: Two points $\mathrm{P}$ and $\mathrm{Q}$ are maintained at the potential of $10 \mathrm{~V}$ and $-4 \mathrm{~V}$, respectively. The work done in moving 100 electrons from $P$ to $Q$ is :-$-2.24 \times 10^{-16} \mathrm{~J}$$2.24 \times 10^{-16} \mathrm{~J}$$-9.60 \times 10^{-17} \mathrm{~J}$$9.60 \times 10^{-17} \mathrm{~J}$Correct Option: , 2 Solution:...
Read More →As an electron makes a transition from an excited state
Question: As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :kinetic energy decreases, potential energy increases but total energy remains samekinetic energy and total energy decrease but potential energy increasesits kinetic energy increases but potential energy and total energy decreaseskinetic energy, potential energy and total energy decrease.Correct Option: , 3 Solution:...
Read More →Statement-1 : For a charged particle moving from point P to point Q
Question: Statement-1 : For a charged particle moving from point $P$ to point $Q$ the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$. Statement-2 : The net work done by a conservative force on an object moving along closed loop is zero.Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not the correct explanation of Statement $-1$Statement-1 is false, Statement $-2$ is trueStatement-1 is true, Statement-2 is fal...
Read More →In a hydrogen like atom electron makes transition from an energy level
Question: In a hydrogen like atom electron makes transition from an energy level with quantum number $\mathrm{n}$ to another with quantum number $(n-1)$. If $n \gg 1$, the frequency of radiation emitted is proportional to: $\frac{1}{n}$$\frac{1}{\mathrm{n}^{2}}$$\frac{1}{n^{3 / 2}}$$\frac{1}{n^{3}}$Correct Option: , 4 Solution:...
Read More →A charge Q is placed at each of the opposite corners of a square.
Question: A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then $\frac{Q}{q}$ equals :-1$-\frac{1}{\sqrt{2}}$$-2 \sqrt{2}$- 1Correct Option: , 3 Solution:...
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