A plane electromagnetic wave of frequency
Question: A plane electromagnetic wave of frequency $100 \mathrm{MHz}$ is travelling in vacuum along the $x-$ direction. At a particular point in space and time, $\overrightarrow{\mathrm{B}}=2.0 \times 10^{-\mathrm{s}} \hat{\mathrm{k}} \mathrm{T} \cdot$ (where, $\hat{\mathrm{k}}$ is unit vector along z-direction) What is $\overrightarrow{\mathrm{E}}$ at this point?$0.6 \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}$$6.0 \hat{\mathrm{k}} \mathrm{V} / \mathrm{m}$$6.0 \hat{j} \mathrm{~V} / \mathrm{m}$$0....
Read More →In thermodynamics, heat and work are :
Question: In thermodynamics, heat and work are :Path functionsIntensive thermodynamic state variablesExtensive thermodynamic state variablesPoint functionsCorrect Option: Solution: Heat and work are treated as path functions in thermodynamics. $\Delta \mathrm{Q}=\Delta \mathrm{U}+\Delta \mathrm{W}$ Since work done by gas depends on type of process i.e. path and 'U depends just on initial and final states, so 'Q i.e. heat, also has to depend on process is path...
Read More →Imagine that the electron in a hydrogen atom
Question: Imagine that the electron in a hydrogen atom is replaced by a muon $(\mu)$. The mass of muon particle is 207 times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be :-$13.6 \mathrm{eV}$$2815.2 \mathrm{eV}$$331.2 \mathrm{eV}$$27.2 \mathrm{eV}$Correct Option: , 2 Solution: $\mathrm{E} \propto \frac{1}{\mathrm{r}}$ $r \propto \frac{1}{m}$ $\mathrm{E} \propto \mathrm{m}$ Ionization potential $=13.6 \times \frac{\lef...
Read More →The volume V of an enclosure contains a mixture of three gases,
Question: The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T. Consider R as universal gas constant. The pressure of the mixture of gases is :$\frac{88 \mathrm{RT}}{\mathrm{V}}$$\frac{3 \mathrm{RT}}{\mathrm{V}}$$\frac{5}{2} \frac{\mathrm{RT}}{\mathrm{V}}$$\frac{4 \mathrm{RT}}{\mathrm{V}}$Correct Option: , 3 Solution: $\mathrm{PV}=\left(\mathrm{n}_{1}+\mathrm{n}_{2}+\mathrm{n}_{3}\right) \mathrm{RT}$...
Read More →Match List-I with List-II.
Question: Match List-I with List-II. List-I (a) $10 \mathrm{~km}$ height over earth's surface (b) $70 \mathrm{~km}$ height over earth's surface (c) $180 \mathrm{~km}$ height over earth's surface (d) $270 \mathrm{~km}$ height over earth's surface List-II (i) Thermosphere (ii) Mesosphere (iii) Stratosphere (iv) Troposphere(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)(a) -(i), (b)-(iv), (c)-(iii), (d)-(ii)(a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)(a) -(ii), (b)-(i), (c)-(iv), (d)-(iii)Correct Option: 1 Soluti...
Read More →A bar magnet of length 14 cm is placed in the magnetic meridian with its north pole pointing towards the geographic north pole.
Question: A bar magnet of length $14 \mathrm{~cm}$ is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at a distance of $18 \mathrm{~cm}$ from the center of the magnet. If $\mathrm{B}_{\mathrm{H}}=0.4 \mathrm{G}$, the$\left.\mathrm{G}=10^{-4} \mathrm{~T}\right)$$2.880 \times 10^{2} \mathrm{~J} \mathrm{~T}^{-1}$$2.880 \mathrm{~J} \mathrm{~T}^{-1}$$28.80 \mathrm{~J} \mathrm{~T}^{-1}$Correct Option: , 3 Solution: i.e. $\frac...
Read More →An oil drop of radius
Question: An oil drop of radius $2 \mathrm{~mm}$ with a density $3 \mathrm{~g}$ $\mathrm{cm}^{-3}$ is held stationary under a constant electric field $3.55 \times 10^{5} \mathrm{~V} \mathrm{~m}^{-1}$ in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (consider $\mathrm{g}=9.81 \mathrm{~m} / \mathrm{s}^{2}$ )$48.8 \times 10^{11}$$1.73 \times 10^{10}$$17.3 \times 10^{10}$$1.73 \times 10^{12}$Correct Option: , 2 Solution: $\mathrm{qE}=\math...
Read More →A point source of light
Question: A point source of light $\mathrm{S}$, placed at a distance $60 \mathrm{~cm}$ infront of the centre of a plane mirror of width $50 \mathrm{~cm}$, hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance $1.2 \mathrm{~m}$ from it (see in the figure). The distance between the extreme points where he can see the image of the light source in the mirror is .......... $\mathrm{cm}$. Solution: $\tan \theta=\frac{25}{60}=\frac{x}{180}$ $x=7...
Read More →Solve this following
Question: Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is $x: y$. The value of $x$ is Solution: $\mathrm{KE}_{\max }=\mathrm{h} v-\phi$ $\frac{1}{2} m v^{2}=h v-\phi$ $v=\sqrt{\frac{2(h v-\phi)}{m}}$ Given $h v_{1}=2 \phi$ $h v_{2}=10 \phi$ $\therefore \frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}=\sqrt{\f...
Read More →If the highest frequency modulating a carrier is
Question: If the highest frequency modulating a carrier is $5 \mathrm{kHz}$, then the number of AM broadcast stations accommodated in a $90 \mathrm{kHz}$ bandwidth are $\ldots \ldots \ldots$ Solution: B. W. (Bandwidth $)=2 \times$ maximum frequency at modulating signal $=2 \times 5 \mathrm{kHz}$ $=10 \mathrm{kHz}$ $\therefore$ No of stations accommodate $=\frac{90}{10}=9$...
Read More →Solve this following
Question: The volume $V$ of a given mass of monoatomic gas changes with temperature $\mathrm{T}$ according to the relation $\mathrm{V}=\mathrm{KT}^{2 / 3}$. The workdone when temperature changes by $90 \mathrm{~K}$ will be $\mathrm{xR}$. The value of $x$ is $[R=$ universal gas constant $]$ Solution: We know that work done is $\mathrm{W}=\int \mathrm{PdV}$ ....(1) $\Rightarrow P=\frac{n R T}{V}$ ..............(2) $\Rightarrow \mathrm{W}=\int \frac{\mathrm{nRT}}{\mathrm{V}} \mathrm{dv}$ .............
Read More →Solve this
Question: If $2.5 \times 10^{-6} \mathrm{~N}$ average force is exerted by a light wave on a non-reflecting surface of $30 \mathrm{~cm}^{2}$ area during 40 minutes of time span, the energy flux of light just before it falls on the surface is _____________ $\mathrm{W} / \mathrm{cm}^{2}$. (Round off to the Nearest Integer) (Assume complete absorption and normal incidence conditions are there) Solution: $\mathrm{F}=\frac{\mathrm{IA}}{\mathrm{C}}$ $\mathrm{I}=\frac{\mathrm{FC}}{\mathrm{A}}=\frac{2.5 ...
Read More →Two blocks
Question: Two blocks $(\mathrm{m}=0.5 \mathrm{~kg}$ and $\mathrm{M}=4.5 \mathrm{~kg})$ are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is $\frac{3}{7}$. Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is__________N. (Round off to the Nearest Integer) [Take g as $9.8 \mathrm{~ms}^{-2}$ ] Solution: $\mathrm{a}_{\max }=\mu \mathrm{g}=\frac{3}{7} \times 9.8$ $\math...
Read More →Solve this following
Question: A wire of $1 \Omega$ has a length of $1 \mathrm{~m}$. It is stetched till its length increases by $25 \%$. The percentage change in resistance to the neartest integer is :-$56 \%$$25 \%$$12.5 \%$$76 \%$Correct Option: 1 Solution: As volume of wire remains constant so $\mathrm{A}_{0} \ell_{0}=\mathrm{A}_{1} \ell_{1} \Rightarrow \mathrm{A}_{1}=\frac{\ell_{0} \mathrm{~A}_{0}}{\ell_{1}}$ Now $\operatorname{Resistance}(\mathrm{R})=\frac{\rho \ell}{\mathrm{A}}$ $\frac{\mathrm{R}_{0}}{\mathrm...
Read More →A parallel plate capacitor
Question: A parallel plate capacitor whose capacitance C is $14 \mathrm{pF}$ is charged by a battery to a potential difference $\mathrm{V}=12 \mathrm{~V}$ between its plates. The charging battery is now disconnected and a porcelin plate with $\mathrm{k}=7$ is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of ___________$\mathrm{pJ}$. (Assume no friction) Solution: $\mathrm{U}_{\mathrm{i}}=\frac{1}{2} \times 14 \time...
Read More →The following bodies,
Question: The following bodies, (1) a ring (2) a disc (3) a solid cylinder (4) a solid sphere, of same mass ' $m$ ' and radius ' $R$ ' are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is [Mark the body as per their respective numbering given in the question] Solution: $M g \sin \theta R=\left(m k^{2}+m R^{2}\right) \alpha$ $\alpha=\frac{\mathrm{Rg} \sin \theta}{\mathrm{k}^{2}+\mathrm{R...
Read More →Given below are two statements :
Question: Given below are two statements : Statement I : A second's pendulum has a time period of 1 second. Statement II : It takes precisely one second to move between the two extreme positions. In the light of the above statements, choose the correct answer from the options given below : Both Statement I and Statement II are false.Statement I is false but Statement II is trueStatement I is true but Statement II is falseBoth Statement I and Statement II are true.Correct Option: , 2 Solution: Se...
Read More →Consider two identical
Question: Consider two identical springs each of spring constant $\mathrm{k}$ and negligible mass compared to the mass $M$ as shown. Fig.1 shows one of them and Fig. 2 shows their series combination. The ratios of time period of oscillation of the two SHM is $\frac{T_{b}}{T_{a}}=\sqrt{x}$, where value of $x$ is (Round off to the Nearest Integer) Solution: $\mathrm{T}_{\mathrm{a}}=2 \pi \sqrt{\frac{\mathrm{M}}{\mathrm{K}}}$ $\mathrm{T}_{\mathrm{b}}=2 \pi \sqrt{\frac{\mathrm{M}}{\mathrm{K} / 2}}$ ...
Read More →A scooter accelerates from rest for time
Question: A scooter accelerates from rest for time $t_{1}$ at constant rate $\mathrm{a}_{1}$ and then retards at constant rate $a_{2}$ for time $t_{2}$ and comes to rest. The correct value of $\frac{t_{1}}{t_{2}}$ will be :-$\frac{a_{1}+a_{2}}{a_{2}}$$\frac{\mathrm{a}_{2}}{\mathrm{a}_{1}}$$\frac{\mathrm{a}_{1}}{\mathrm{a}_{2}}$$\frac{a_{1}+a_{2}}{a_{1}}$Correct Option: , 2 Solution: Draw vt curve $\tan \theta_{1}=a_{1}=\frac{v_{\max }}{t_{1}}$ $\ \tan \theta_{2}=\mathrm{a}_{2}=\frac{\mathrm{v}_{...
Read More →Two particles having masses
Question: Two particles having masses $4 \mathrm{~g}$ and $16 \mathrm{~g}$ respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is $\mathrm{n}: 2$. The value of $\mathrm{n}$ will be_________. Solution: $\frac{\mathrm{p}_{1}^{2}}{2 \times 4}=\frac{\mathrm{p}_{2}^{2}}{2 \times 16}$ $\frac{p_{1}}{p_{2}}=\frac{1}{2}$...
Read More →A current of 6 A enters one corner P of an equilateral
Question: A current of 6 A enters one corner $P$ of an equilateral triangle $P Q R$ having 3 wires of resistance $2 \Omega$ each and leaves by the corner $R$. The currents $i_{1}$ in ampere is_________. Solution: For parallel combination current devides in the inverse ratio of resistance. $\mathrm{i}_{\mathrm{PQ}}=\frac{2}{6} \times 6 \mathrm{~A}$...
Read More →The radius in kilometer
Question: The radius in kilometer to which the present radius of earth $(R=6400 \mathrm{~km})$ to be compressed so that the escape velocity is increased 10 time is Solution: $\mathrm{V}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{Gm}}{\mathrm{R}}}$.....(1) $10 \mathrm{~V}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{Gm}}{\mathrm{R}^{\prime}}} \ldots$ (2) $\therefore 10=\sqrt{\frac{\mathrm{R}}{\mathrm{R}^{\prime}}}$ $\Rightarrow R^{\prime}=\frac{R}{100}=\frac{6400}{100}=64 \mathrm{~km}$...
Read More →Two identical conducting spheres with negligible
Question: Two identical conducting spheres with negligible volume have $2.1 \mathrm{nC}$ and $-0.1 \mathrm{nC}$ charges, respectively. They are brought into contact and then separated by a distance of $0.5 \mathrm{~m}$. The electrostatic force acting between the spheres is__________ $\times 10^{-9} \mathrm{~N}$. [Given : $4 \pi \varepsilon_{0}=\frac{1}{9 \times 10^{9}}$ SI unit] Solution: $\mathrm{q}=\frac{(2.1-0.1)}{2} \mathrm{nC}=1 \mathrm{nC}$ $f=\frac{9 \times 10^{9} \times 10^{-18}}{(0.5)^{...
Read More →A radioactive sample is undergoing
Question: A radioactive sample is undergoing $\alpha$ decay. At any time $\mathrm{t}_{1}$, its activity is A and another time $t_{2}$, the activity is $\frac{\mathrm{A}}{5}$. What is the average life time for the sample ? $\frac{\ell \mathrm{n} 5}{\mathrm{t}_{2}-\mathrm{t}_{1}}$$\frac{t_{1}-t_{2}}{\ell n 5}$$\frac{\mathrm{t}_{2}-\mathrm{t}_{1}}{\ell \operatorname{n} 5}$$\frac{\ln \left(\mathrm{t}_{2}+\mathrm{t}_{1}\right)}{2}$Correct Option: , 3 Solution: Let initial activity be $\mathrm{A}_{0}$...
Read More →Four identical rectangular
Question: Four identical rectangular plates with length, $l=2 \mathrm{~cm}$ and breadth, $\mathrm{b}=\frac{3}{2} \mathrm{~cm}$ are arranged as shown in figure. The equivalent capacitance between $\mathrm{A}$ and $\mathrm{C}$ is $\frac{\mathrm{x} \varepsilon_{0}}{\mathrm{~d}}$. The value of $\mathrm{x}$ is _____________ (Round off to the Nearest Integer) Solution: $\mathrm{C}_{\mathrm{eq}}=\frac{2 \mathrm{C}_{0}}{3}=\frac{2}{3} \frac{\mathrm{E}_{0} \mathrm{~A}}{\mathrm{~d}}$ $\mathrm{C}_{\mathrm{...
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