The thickness at the centre
Question: The thickness at the centre of a plano convex lens is $3 \mathrm{~mm}$ and the diameter is $6 \mathrm{~cm}$. If the speed of light in the material of the lens is $2 \times 10^{8} \mathrm{~ms}^{-1}$. The focal length of the lens is _______.$0.30 \mathrm{~cm}$$15 \mathrm{~cm}$$1.5 \mathrm{~cm}$$30 \mathrm{~cm}$Correct Option: , 4 Solution: $R^{2}=r^{2}+(R-t)^{2}$ $R^{2}=r^{2}+R^{2}+t^{2}-2 R t$ Neglecting $t^{2}$, we get $R=\frac{r^{2}}{2 t}$ $\therefore \frac{1}{f}=(\mu-1)\left(\frac{1}...
Read More →A Carnot's engine
Question: A Carnot's engine working between $400 \mathrm{~K}$ and $800 \mathrm{~K}$ has a work output of $1200 \mathrm{~J}$ per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :$3200 \mathrm{~J}$$1800 \mathrm{~J}$$1600 \mathrm{~J}$$2400 \mathrm{~J}$Correct Option: , 4 Solution: $\eta=\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\frac{\mathrm{Q}_{2}}{\mathrm{Q}_{1}}=\frac{\mathrm{Q}_{1}-\mathrm{W}}{\mathrm{Q}_{1}}$ $\left(\because \mathrm{W}=\mathrm{Q}_{1}-\math...
Read More →The point A moves with a uniform speed along the circumference
Question: The point A moves with a uniform speed along the circumference of a circle of radius $0.36 \mathrm{~m}$ and covers $30^{\circ}$ in $0.1 \mathrm{~s}$. The perpendicular projection ' $\mathrm{P}$ ' from 'A' on the diameter $\mathrm{MN}$ represents the simple harmonic motion of ' $P$ '. The restoration force per unit mass when $P$ touches $M$ will be : $100 \mathrm{~N}$$0.49 \mathrm{~N}$$50 \mathrm{~N}$$9.87 \mathrm{~N}$Correct Option: , 4 Solution: $30^{\circ} \rightarrow 0.1 \mathrm{~s}...
Read More →For what value of displacement
Question: For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?$x=0$$x=\pm A$$x=\pm \frac{A}{\sqrt{2}}$$x=\frac{A}{2}$Correct Option: , 3 Solution: $\mathrm{KE}=\mathrm{PE}$ $\frac{1}{2} m \omega^{2}\left(A^{2}-x^{2}\right)=\frac{1}{2} m \omega^{2} x^{2}$ $A^{2}-x^{2}=x^{2}$ $2 x^{2}=A^{2}$ $x=\pm \frac{A}{\sqrt{2}}$...
Read More →Given below are two statements :
Question: Given below are two statements : Statement I : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero but the electric field is not zero anywhere in the sphere. Statement II : If $R$ is the radius of a solid metallic sphere and $\mathrm{Q}$ be the total charge on it. The electric field at any point on the spherical surface of radius $r(R)$ is zero but the electric flux passing through this closed spherical surface of radius ...
Read More →A mass M hangs on a massless
Question: A mass $M$ hangs on a massless rod of length $l$ which rotates at a constant angular frequency. The mass $M$ moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity $\omega$. The angular momentum of $M$ about point $A$ is $L_{A}$ which lies in the positive $z$ direction and the angular momentum of $M$ about $B$ is $L_{B}$. The correct statement for this system is : $\mathrm{L}_{\mathrm{A}}$ and $\...
Read More →An electron with kinetic energy
Question: An electron with kinetic energy $K_{1}$ enters between parallel plates of a capacitor at an angle ' $\alpha$ ' with the plates. It leaves the plates at angle ' $\beta$ ' with kinetic energy $K_{2}$. Then the ratio of kinetic energies $K_{1}: K_{2}$ will be :$\frac{\sin ^{2} \beta}{\cos ^{2} \alpha}$$\frac{\cos ^{2} \beta}{\cos ^{2} \alpha}$$\frac{\cos \beta}{\cos \alpha}$$\frac{\cos \beta}{\sin \alpha}$Correct Option: , 2 Solution: velocity along the plate will not change. $\therefore ...
Read More →A solenoid of 1000 turns
Question: A solenoid of 1000 turns per metre has a core with relative permeability 500 . Insulated windings of the solenoid carry an electric current of $5 \mathrm{~A}$. The magnetic flux density produced by the solenoid is : (permeability of free space $=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$ )$\pi \mathrm{T}$$2 \times 10^{-3} \pi \mathrm{T}$$\frac{\pi}{5} \mathrm{~T}$$10^{-4} \pi \mathrm{T}$Correct Option: 1 Solution: $\mathrm{B}=\mu \mathrm{nI}=\mu_{0} \mu_{\mathrm{r}} \mathrm{nI}$ $\m...
Read More →Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Question: Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : For a simple microscope, the angular size of the object equals the angular size of the image. Reason R : Magnification is achieved as the small object can be kept much closer to the eye than $25 \mathrm{~cm}$ and hence it subtends a large angle. In the light of the above statements, choose the most appropriate answer from the options given below :A is true but $R$ is fal...
Read More →If e is the electronic charge, c is the speed
Question: If $e$ is the electronic charge, $c$ is the speed of light in free space and $\mathrm{h}$ is Planck's constant, the quantity $\frac{1}{4 \pi \varepsilon_{0}} \frac{|\mathrm{e}|^{2}}{h c}$ has dimensions of :$\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]$$\left[\mathrm{L} \mathrm{C}^{-1}\right]$$\left[\mathrm{M} \mathrm{L} \mathrm{} \mathrm{T}^{-1}\right]$$[\mathrm{M} \mathrm{L} \mathrm{T}$ ]Correct Option: 1 Solution: $\mathrm{F}=\frac{1}{4 \pi \epsilon_{0}} \frac{\mathrm...
Read More →A car accelerates from
Question: A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is $t$ seconds, the total distance travelled is :$\frac{4 \alpha \beta}{(\alpha+\beta)} \mathrm{t}^{2}$$\frac{2 \alpha \beta}{(\alpha+\beta)} \mathrm{t}^{2}$$\frac{\alpha \beta}{2(\alpha+\beta)} t^{2}$$\frac{\alpha \beta}{4(\alpha+\beta)} \mathrm{t}^{2}$Correct Option: , 3 Solution: $\mathrm{v}_{0}=\alpha \mathrm{t}_{1}$ ...
Read More →Solve this following
Question: The internal energy (U), pressure $(P)$ and volume $(\mathrm{V})$ of an ideal gas are related as $\mathrm{U}=$ $3 \mathrm{PV}+4$. The gas is :-Diatomic onlyPolyatomic onlyEither monoatomic or diatomicMonoatomic onlyCorrect Option: , 2 Solution: $\mathrm{U}=3 \mathrm{PV}+4$ $\frac{\mathrm{nf}}{2} \mathrm{RT}=3 \mathrm{PV}+4$ $\frac{f}{2} P V=3 P V+4$ $f=6+\frac{8}{P V}$...
Read More →Y = A sin (ωt + Φ0) is the time-displacement equation
Question: $\mathrm{Y}=\mathrm{A} \sin \left(\omega \mathrm{t}+\phi_{0}\right)$ is the time-displacement equation of a SHM. At $t=0$ the displacement of the particle is $Y=\frac{A}{2}$ and it is moving along negative $x$-direction. Then the initial phase angle $\phi_{0}$ will be :$\frac{\pi}{6}$$\frac{\pi}{3}$$\frac{5 \pi}{6}$$\frac{2 \pi}{3}$Correct Option: , 3 Solution: initial phase $\frac{\pi}{2}+\frac{\pi}{3}=\frac{5 \pi}{6}$...
Read More →A modern grand-prix
Question: A modern grand-prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius $R$ with a speed $v$. If the coefficient of static friction between the tyres and the track is $\mu_{\mathrm{s}}$, then the magnitude of negative lift $\mathrm{F}_{\mathrm{L}}$ acting downwards on the car is : (Assume forces on the four tyres are identical and $g=$ acceleration due to gravity) $\mathrm{m}\left(\frac{\mathrm{v}^{2}}{\mu_{\mathrm{s}} \mathrm{R}}+\mathrm{g}\right)$$m\left(...
Read More →A cord is wound round the circumference of wheel of radius
Question: A cord is wound round the circumference of wheel of radius $\mathrm{r}$. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight $\mathrm{mg}$ is attached to the cord at the end. The weight falls from rest. After falling through a distance ' $h$ ', the square of angular velocity of wheel will be :-$\frac{2 m g h}{\mathrm{I}+2 \mathrm{mr}^{2}}$$\frac{2 m g h}{I+m r^{2}}$$2 \mathrm{gh}$$\frac{2 g h}{I+m r^{2}}$Correct Option: , 3 Solution: $m g h=\frac{1}{2}...
Read More →An AC current is given
Question: An AC current is given by $I=I_{1} \sin \omega t+I_{2} \cos \omega t$. A hot wire ammeter will give a reading :$\sqrt{\frac{\mathrm{I}_{1}^{2}-\mathrm{I}_{2}^{2}}{2}}$$\sqrt{\frac{\mathrm{I}_{1}^{2}+\mathrm{I}_{2}^{2}}{2}}$$\frac{\mathrm{I}_{1}+\mathrm{I}_{2}}{\sqrt{2}}$$\frac{\mathrm{I}_{1}+\mathrm{I}_{2}}{2 \sqrt{2}}$Correct Option: , 2 Solution: $I=I_{1} \sin \omega t+I_{2} \cos \omega t$ $\therefore \mathrm{I}_{0}=\sqrt{\mathrm{I}_{1}^{2}+\mathrm{I}_{2}^{2}}$ $\therefore \mathrm{I}...
Read More →An electron of mass m_e and a proton of mass
Question: An electron of mass $m_{e}$ and a proton of mass $m_{p}=1836 \mathrm{~m}_{\mathrm{e}}$ are moving with the same speed. The ratio of their de Broglie wavelength $\frac{\lambda_{\text {eectron }}}{\lambda_{\text {proton }}}$ will be :18361918$\frac{1}{1836}$Correct Option: 1 Solution: $\frac{\lambda_{e}}{\lambda_{p}}=\frac{\frac{\mathrm{h}}{\mathrm{m}_{e} \mathrm{v}}}{\frac{\mathrm{h}}{\mathrm{m}_{\mathrm{p}} \mathrm{v}}}=1836$...
Read More →The trajectory of a projectile in a vertical plane is
Question: The trajectory of a projectile in a vertical plane is $\mathrm{y}=\alpha \mathrm{x}-\beta \mathrm{x}^{2}$, where $\alpha$ and $\beta$ are constants and $x$ \ $y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained $\mathrm{H}$ are respectively given by :-$\tan ^{-1} \alpha, \frac{\alpha^{2}}{4 \beta}$$\tan ^{-1} \beta, \frac{\alpha^{2}}{2 \beta}$$\tan ^{-1} \alpha, \frac{...
Read More →The vernier scale
Question: The vernier scale used for measurement has a positive zero error of $0.2 \mathrm{~mm}$. If while taking a measurement it was noted that ' 0 ' on the vernier scale lies between $8.5 \mathrm{~cm}$ and $8.6 \mathrm{~cm}$, vernier coincidence is 6 , then the correct value of measurement is __________ $\mathrm{cm}$.$8.36 \mathrm{~cm}$$8.54 \mathrm{~cm}$$8.58 \mathrm{~cm}$$8.56 \mathrm{~cm}$Correct Option: , 2 Solution: Positive zero error $=0.2 \mathrm{~mm}$ Main scale reading $=8.5 \mathrm...
Read More →A sphere of radius ' a ' and mass ' m ' rolls along
Question: A sphere of radius ' $a$ ' and mass ' $m$ ' rolls along a horizontal plane with constant speed $v_{0}$. It encounters an inclined plane at angle $\theta$ and climbs upward. Assuming that it rolls without slipping, how far up the sphere will travel ? $\frac{10 v_{0}^{2}}{7 g \sin \theta}$$\frac{v_{0}^{2}}{5 g \sin \theta}$$\frac{2}{5} \frac{v_{0}^{2}}{g \sin \theta}$$\frac{v_{0}^{2}}{2 g \sin \theta}$Correct Option: 1 Solution: Angular momentum conservation about A $\mathrm{mv}_{0} \mat...
Read More →Two identical metal
Question: Two identical metal wires of thermal conductivities $\mathrm{K}_{1}$ and $\mathrm{K}_{2}$ respectively are connected in series. The effective thermal conductivity of the combination is :$\frac{2 \mathrm{~K}_{1} \mathrm{~K}_{2}}{\mathrm{~K}_{1}+\mathrm{K}_{2}}$$\frac{\mathrm{K}_{1}+\mathrm{K}_{2}}{2 \mathrm{~K}_{1} \mathrm{~K}_{2}}$$\frac{\mathrm{K}_{1}+\mathrm{K}_{2}}{\mathrm{~K}_{1} \mathrm{~K}_{2}}$$\frac{\mathrm{K}_{1} \mathrm{~K}_{2}}{\mathrm{~K}_{1}+\mathrm{K}_{2}}$Correct Option:...
Read More →A particle executes S.H.M., the graph of velocity as a function of displacement is :-
Question: A particle executes S.H.M., the graph of velocity as a function of displacement is :-A circleA parabolaAn ellipseA helixCorrect Option: , 3 Solution: $v^{2}=\omega^{2}\left(A^{2}-x^{2}\right)$ $\frac{v^{2}}{\omega^{2}}+x^{2}=A^{2}$ $\frac{v^{2}}{(\omega A)^{2}}+\frac{x^{2}}{A^{2}}=1$ This is an equation of an ellipse....
Read More →An electron of mass
Question: An electron of mass $m$ and a photon have same energy E. The ratio of wavelength of electron to that of photon is: (c being the velocity of light)$\frac{1}{c}\left(\frac{2 m}{E}\right)^{1 / 2}$$\frac{1}{c}\left(\frac{E}{2 m}\right)^{1 / 2}$$\left(\frac{E}{2 m}\right)^{1 / 2}$c $(2 m E)^{1 / 2}$Correct Option: , 2 Solution: $\lambda_{1}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}$ $\lambda_{2}=\frac{\mathrm{hc}}{\mathrm{E}}$ $\frac{\lambda_{1}}{\lambda_{2}}=\frac{1}{\mathrm{c}}\left(\frac{\...
Read More →If an electron is moving
Question: If an electron is moving in the $\mathrm{n}^{\text {th }}$ orbit of the hydrogen atom, then its velocity $\left(v_{n}\right)$ for the $n^{\text {th }}$ orbit is given as :$v_{n} \propto n$$\mathrm{v}_{\mathrm{n}} \propto \frac{1}{\mathrm{n}}$$v_{n} \propto n^{2}$$v_{n} \propto \frac{1}{n^{2}}$Correct Option: , 2 Solution: We know velocity of electron in $n^{\text {th }}$ shell of hydrogen atom is given by $\mathrm{v}=\frac{2 \pi k Z \mathrm{e}^{2}}{\mathrm{nh}}$ $\therefore \mathrm{v} ...
Read More →Solve this following
Question: A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency $340 \mathrm{~Hz}$. When fork $\mathrm{A}$ is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A ?$342 \mathrm{~Hz}$$345 \mathrm{~Hz}$$335 \mathrm{~Hz}$$338 \mathrm{~Hz}$Correct Option: , 3 Solution: Initially beat frequency $=5 \mathrm{~Hz}$ so, $\rho_{\mathrm{A}}=340 \pm 5=345 \mathrm{~Hz}$, or $335 \mathrm{~Hz}$ after filing frequency increases slightly so, new value...
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