Explore topic-wise MCQs in Joint Entrance Exam - Main (JEE Main).

This section includes 12583 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.

2751.

A total charge Q is broken in two parts \[{{Q}_{1}}\] and \[{{Q}_{2}}\] and they are placed at a distance R from each

A. \[{{Q}_{2}}=\frac{Q}{R},{{Q}_{1}}=Q-\frac{Q}{R}\] 
B. \[{{Q}_{2}}=\frac{Q}{4},{{Q}_{1}}=Q-\frac{2Q}{3}\]
C. \[{{Q}_{2}}=\frac{Q}{4},{{Q}_{1}}=\frac{3Q}{4}\]                           
D. \[{{Q}_{1}}=\frac{Q}{2},{{Q}_{2}}=\frac{Q}{2}\]
Answer» E.
2752.

Two equal point charges each of \[3\mu C\] are separated by a certain distance in meters. If they are located at \[(\hat{i}+\hat{j}+\hat{k})\] and \[(2\hat{i}+3\hat{j}+\hat{k})\], then the electrostatic force between them is

A. \[9\times {{10}^{3}}N\]
B. \[16\times {{10}^{-3}}N\]
C. \[{{10}^{-3}}N\]
D. \[9\times {{10}^{-2}}N\]
Answer» C. \[{{10}^{-3}}N\]
2753.

Two pith balls carrying equal charges are suspended from a common point by strings of equal the balls now become       

A. \[\left( \frac{r}{\sqrt[3]{2}} \right)\]          
B.        \[\left( \frac{2r}{\sqrt{3}} \right)\]
C. \[\left( \frac{2r}{3} \right)\]         
D.        \[{{\left( \frac{r}{\sqrt{2}} \right)}^{2}}\]
Answer» B.        \[\left( \frac{2r}{\sqrt{3}} \right)\]
2754.

Among two discs A and B, first have radius 10 cn and charge \[{{10}^{-6}}\mu C\]and second have radius 30 cm and charge \[{{10}^{-5}}C.\] When they are touched, charge on both \[{{q}_{A}}\]and \[{{q}_{B}}\]respectively will, be

A. \[{{q}_{A}}=2.75\mu C,{{q}_{B}}=3.15\mu C\]
B. \[{{q}_{A}}=1.09\mu C,{{q}_{B}}=5.5\mu C\]
C. \[{{q}_{A}}={{q}_{B}}=5.5\mu C\]
D. None of these
Answer» D. None of these
2755.

The force of repulsion between two electrons at a certain distance is F. The force between two protons separated by the same distance is \[({{m}_{p}}=1836{{m}_{e}})\]

A. 2F
B. F    
C. 1836F
D. \[\frac{F}{1836}\]
Answer» C. 1836F
2756.

Three charges \[{{q}_{1}},\text{ }+{{q}_{2}}\] and \[{{q}_{3}}\]are place as shown in the figure. The x-component of the force on\[-{{q}_{1}}\]is proportional to

A. \[\frac{{{q}_{2}}}{{{b}^{2}}}-\frac{{{q}_{3}}}{{{a}^{2}}}\cos \theta \]
B. \[\frac{{{q}_{2}}}{{{b}^{2}}}+\frac{{{q}_{3}}}{{{a}^{2}}}\sin \theta \]
C.  \[\frac{{{q}_{2}}}{{{b}^{2}}}+\frac{{{q}_{3}}}{{{a}^{2}}}\cos \theta \]
D. \[\frac{{{q}_{2}}}{{{b}^{2}}}-\frac{{{q}_{3}}}{{{a}^{2}}}\sin \theta \]  
Answer» C.  \[\frac{{{q}_{2}}}{{{b}^{2}}}+\frac{{{q}_{3}}}{{{a}^{2}}}\cos \theta \]
2757.

ggTwo particles A and B having equal charges are placed at a distance d apart. A third charged particle placed on the perpendicular bisection of AB at distance x. The third particle experiences maximum force when

A. \[x=\frac{d}{\sqrt{2}}\]
B. \[x=\frac{d}{2}\]
C. \[x=\frac{d}{2\sqrt{2}}\]
D. \[x=\frac{d}{3\sqrt{2}}\]
Answer» D. \[x=\frac{d}{3\sqrt{2}}\]
2758.

A charged ball B hangs from a silk thread S, which makes an angle \[\theta \] with a large charged conducting sheet P, as shown in the figure. The surface charge density \[\sigma \] of the sheet is proportional to

A. \[\cot \theta \]
B. \[\cos \theta \]
C. \[\tan \theta \]
D. \[\sin \theta \]
Answer» D. \[\sin \theta \]
2759.

A large no conducting sheet M is given a uniform charge density. Two uncharged small metal rods A and B are placed near the sheet as shown in figure. Then

A. M attracts A
B. M attracts B
C. A attracts B
D. All of these
Answer» E.
2760.

The electric charge required to expand a soap bubble to twice its dimension is

A. \[8\pi \sqrt{{{\in }_{0}}\,{{r}^{3}}(7\Pr +12T)}\]         
B. \[8\pi \sqrt{{{\in }_{0}}{{r}^{2}}(7\Pr +12T)}\]
C. \[8\pi \sqrt{{{\in }_{0}}{{r}^{3}}(6\Pr +12T)}\]
D. \[\ell \]
Answer» B. \[8\pi \sqrt{{{\in }_{0}}{{r}^{2}}(7\Pr +12T)}\]
2761.

The metal knob of a gold leaf electroscope is touched with a positively charged rod. When it is taken away the leaves stay separated. Now the metal knob is touched by negatively charged rod. The separation between the leaves

A. increases             
B. decreases
C. remains same
D. first increases then decreases.
Answer» C. remains same
2762.

The figure shows a charge +q at point P held in equilibrium in air with the help of four +q charges situated at the vertices of a square. The net electrostatic force on q is given by

A. Newton's
B. Coulomb's law
C. Principle of superposition
D. Net electric flux out the position of +q.
Answer» D. Net electric flux out the position of +q.
2763.

One-fourth of a sphere of radius R is removed as shown in Fig. An electric field E exists parallel to the xy plane. Find the flux through the curved part.

A. \[\pi {{R}^{2}}E\]
B. \[\sqrt{2}\pi {{R}^{2}}E\]
C. \[\pi {{R}^{2}}E/\sqrt{2}\]
D. None of these
Answer» D. None of these
2764.

1 C charge is equivalent to charge on how much number of protons?

A. \[6\times {{10}^{18}}\]           
B.        \[7\times {{10}^{19}}\]
C. \[8\times {{10}^{20}}\]           
D.        \[9\times {{10}^{21}}\]
Answer» B.        \[7\times {{10}^{19}}\]
2765.

Two identical non-relative particles A and B move right angles to each other, processing de Broglie wavelength \[{{\lambda }_{1}}\] and \[\,{{\lambda }_{2}}\], respectively. The de Broglie wavelength of each particle in their center of mass frame of reference is

A. \[{{\lambda }_{1}}+{{\lambda }_{2}}\]
B. \[2{{\lambda }_{1}}{{\lambda }_{2}}/\left( \sqrt{\lambda _{1}^{2}+\lambda _{2}^{2}} \right)\]
C. \[2{{\lambda }_{1}}{{\lambda }_{2}}/\left( \sqrt{\left| \lambda _{1}^{2}+\lambda _{2}^{2} \right|} \right)\]
D. \[\left( {{\lambda }_{1}}+{{\lambda }_{2}} \right)/2\]
Answer» C. \[2{{\lambda }_{1}}{{\lambda }_{2}}/\left( \sqrt{\left| \lambda _{1}^{2}+\lambda _{2}^{2} \right|} \right)\]
2766.

The ratio of the \[{{\lambda }_{\min }}\]in a Coolidge tube to \[{{\lambda }_{deBroglie}}\] of the electrons striking the target depends on accelerating potential V as

A. \[\frac{{{\lambda }_{\min }}}{{{\lambda }_{deBroglie}}}\propto \sqrt{V}\]
B. \[\frac{{{\lambda }_{\min }}}{{{\lambda }_{deBroglie}}}\propto V\]
C. \[\frac{{{\lambda }_{\min }}}{{{\lambda }_{deBroglie}}}\propto \frac{1}{\sqrt{V}}\]
D. \[\frac{{{\lambda }_{\min }}}{{{\lambda }_{deBroglie}}}\propto \frac{1}{V}\]
Answer» D. \[\frac{{{\lambda }_{\min }}}{{{\lambda }_{deBroglie}}}\propto \frac{1}{V}\]
2767.

The shortest wavelength of X-ray emitted from an X-ray tube operated at \[2\times {{10}^{6}}volt\]is of the order of

A. \[{{10}^{-5}}\overset{\text{o}}{\mathop{\text{A}}}\,\]
B. \[1.852\overset{\text{o}}{\mathop{\text{A}}}\,\]
C. \[0.5\overset{\text{o}}{\mathop{\text{A}}}\,\]
D. \[0.7\overset{\text{o}}{\mathop{\text{A}}}\,\]
Answer» C. \[0.5\overset{\text{o}}{\mathop{\text{A}}}\,\]
2768.

De-Broglie wavelength associated with the hydrogen atom moving with most probable velocity at \[27{}^\circ C\] is \[1.26\overset{\text{o}}{\mathop{\text{A}}}\,\]. De-Broglie wavelength associated with helium atom moving with r.m.s. velocity at \[51{}^\circ C\] is:

A. \[2.268\overset{\text{o}}{\mathop{\text{A}}}\,\]
B. \[1.852\overset{\text{o}}{\mathop{\text{A}}}\,\]
C. \[0.5\overset{\text{o}}{\mathop{\text{A}}}\,\]
D. \[0.7\overset{\text{o}}{\mathop{\text{A}}}\,\]
Answer» D. \[0.7\overset{\text{o}}{\mathop{\text{A}}}\,\]
2769.

To decrease the cut-off wavelength of continuous X-rays by 25%, the potential difference across X-ray tube

A. must be increased by \[\frac{100}{3}%\]
B. must be decreased by \[\frac{100}{3}%\]
C. must increased by 25%
D. must decreased by 25%.
Answer» B. must be decreased by \[\frac{100}{3}%\]
2770.

A material particle with a rest mass \[{{m}_{0}}\]is moving with a velocity of light c. Then the wavelength of the de Broglie wave associated with is is:

A. \[\left( h/{{m}_{0}}c \right)\]
B. zero
C. \[\infty \]
D. \[\left( {{m}_{0}}c/h \right)\]
Answer» C. \[\infty \]
2771.

Photoelectric emission is observed from a metallic surface for frequencies \[{{v}_{1}}\] and \[{{v}_{2}}\] of the incident light rays\[\left( {{v}_{1}}>{{v}_{2}} \right)\]. If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio of 1:k, then the threshold frequency of the metallic surface is

A. \[\frac{{{v}_{1}}-{{v}_{2}}}{k-1}\]
B. \[\frac{k{{v}_{1}}-{{v}_{2}}}{k-1}\]
C. \[\frac{k{{v}_{2}}-{{v}_{1}}}{k-1}\]
D. \[\frac{{{v}_{2}}-{{v}_{1}}}{k-1}\]
Answer» C. \[\frac{k{{v}_{2}}-{{v}_{1}}}{k-1}\]
2772.

The de Broglie wavelength of an electron is the same as that of a 50 KeV X-ray photon. The ratio of the energy of the photon to the kinetic energy of the electron is: (the energy equivalent of electron mass is 0.5 MeV)

A. 1 : 50 
B. 1 : 20  
C. 0.834027777777778
D. 2.08402777777778
Answer» D. 2.08402777777778
2773.

A 200 W sodium street lamp emits yellow light of wavelength \[0.6\,\mu m\]. Assuming it to be 25% efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is

A. \[1.5\times {{10}^{20}}\]
B. \[6\times {{10}^{18}}\]
C. \[62\times {{10}^{20}}\]
D. \[3\times {{10}^{19}}\]
Answer» B. \[6\times {{10}^{18}}\]
2774.

A photoelectric surface is illuminated successively by monochromatic light of wavelengths \[\lambda \] and\[\frac{\lambda }{2}.\] If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface is:

A. \[\frac{hc}{2\lambda }\]
B. \[\frac{hc}{\lambda }\]
C. \[\frac{hc}{3\lambda }\]
D. \[\frac{3hc}{\lambda }\]
Answer» B. \[\frac{hc}{\lambda }\]
2775.

A proton has kinetic energy E = 100 keV which is equal to that of a photon. The wavelength of photon is \[{{\lambda }_{2}}\] and that of proton is \[{{\lambda }_{1}}.\] The ration of \[{{\lambda }_{2}}/{{\lambda }_{1}}\] is proportional to

A. \[{{E}^{2}}\]
B. \[{{E}^{1/2}}\]
C. \[{{E}^{-1}}\] 
D. \[{{E}^{-1/2}}\]
Answer» E.
2776.

A point source causes photoelectric effect from a small metal plate. Which of the curves in Fig may represent the saturation photo - current as a function of the distance between the source and the metal?

A.
B. B   
C. C
D. D
Answer» E.
2777.

A perfectly reflecting solid sphere of radius x is kept in the path of a parallel beam of light of large aperture. If the beam carries an intensity I, find the force exerted by the beam on the sphere.

A. \[\frac{\pi {{x}^{2}}i}{C}\]
B. \[\frac{\pi {{x}^{3}}{{i}^{2}}}{2C}\]
C. \[\frac{\pi x{{i}^{2}}}{2C}\]
D. \[\frac{3\pi {{x}^{2}}i}{C}\]
Answer» B. \[\frac{\pi {{x}^{3}}{{i}^{2}}}{2C}\]
2778.

A parallel beam of light of wavelength 600 nm and intensity \[100\text{ }w\text{ }{{m}^{-2}}\]. How many photons cross \[1\text{ }c{{m}^{2}}\] area perpendicular to the beam in 1 sec?

A. \[3.0\times {{10}^{16}}\]
B. \[4.0\times {{10}^{15}}\]
C. \[2.0\times {{10}^{14}}\]
D. \[1.0\times {{10}^{13}}\]
Answer» B. \[4.0\times {{10}^{15}}\]
2779.

The maximum kinetic energy of photoelectrons emitted from a surface when photons of energy 6 eV fall on it is 4 eV. The stopping potential, in volt, is

A. 2
B. 4    
C. 6
D. 10
Answer» C. 6
2780.

In a photo-emissive cell, with exciting wavelength X, the fastest electron has speed v. If the exciting wavelength is changed to \[\frac{5\lambda }{4}\], the speed of the fastest emitted electron will be

A. \[{{\left( 3/4 \right)}^{1/2}}.v~\]           
B. \[{{\left( 4/5 \right)}^{1/2}}.v\]
C. less than \[{{\left( 4/5 \right)}^{1/2}}.v\]
D. greater than \[{{\left( 4/5 \right)}^{1/2}}.v\]
Answer» E.
2781.

For photoelectric emission from certain metal the cut-off frequency is v. If radiation of frequency 2v impinges on the metal plate, the maximum possible velocity of the emitted electron will be (m is the electron mass)

A. \[\sqrt{hv/m}\]
B. \[\sqrt{2hv/m}\]
C. \[2\sqrt{hv/m}\]
D. \[\sqrt{hv/\left( 2m \right)}\]
Answer» C. \[2\sqrt{hv/m}\]
2782.

Electromagnetic radiation falls on a metallic body whose work function is 2eV. For a particular radiation of frequency v, the maximum kinetic energy of the photoelectron is found to be 4 eV. What would be the maximum kinetic energy of 5v photoelectron for the radiation of frequency\[\frac{5v}{3}\] ?

A. \[\frac{8}{3}eV\]                       
B. \[8eV\]
C. \[\frac{10}{3}eV\]                     
D. \[\frac{20}{3}eV\]
Answer» C. \[\frac{10}{3}eV\]                     
2783.

The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is: \[\left( hc=1240eV.nm \right)\]

A. 1.41 eV
B. 1.51 eV
C. 1.68 eV
D. 3.09 eV
Answer» B. 1.51 eV
2784.

An electron microscope uses electrons accelerated by a voltage of 50 kV. If \[\lambda \] be the de-Broglie wavelength associated with the electrons. Also taking other factors, such as numerical aperture etc. to be same, the resolving power of an electron microscope be Re & that of an optical microscope which used yellow light is

A. \[\lambda =0.05\overset{\text{o}}{\mathop{\text{A}}}\,,{{R}_{e}}>>{{R}_{o}}\]         
B. \[\lambda =0.15\overset{\text{o}}{\mathop{\text{A}}}\,,{{R}_{e}}<<{{R}_{o}}\]
C. \[\lambda =0.11\overset{\text{o}}{\mathop{\text{A}}}\,,{{R}_{e}}<{{R}_{o}}\]
D. None of these
Answer» B. \[\lambda =0.15\overset{\text{o}}{\mathop{\text{A}}}\,,{{R}_{e}}<<{{R}_{o}}\]
2785.

\[{{10}^{-3}}W\] of \[\text{5000}\overset{\text{o}}{\mathop{\text{A}}}\,\]light is directed on a photoelectric cell. If the current in the cell is\[0.16\mu A\]. The percentage of incident photons which produce photoelectrons, is

A. 0.004
B. 0.0004
C. 20%     
D. 0.1
Answer» C. 20%     
2786.

A metal surface is illuminated by a light of given intensity and frequency to cause photoemission. If the intensity of illumination is reduced to one-fourth of its original value, then the maximum KE, of emitted photoelectrons will become

A. (1/16)th of original value
B. unchanged
C. twice the original value               
D. four times the original value
Answer» C. twice the original value               
2787.

Light of wavelength 500 nm is incident on a metal with work function 2.28 eV. The wavelength of the emitted electron is:

A. \[<2.8\times {{10}^{-9}}m\]
B. \[\ge 2.8\times {{10}^{-9}}m\]
C. \[\le 2.8\times {{10}^{-12}}m\]
D. \[<2.8\times {{10}^{-10}}m\]
Answer» C. \[\le 2.8\times {{10}^{-12}}m\]
2788.

The threshold frequency for a metallic surfaces corresponds on an energy of 6.2 eV and the stopping potential for a radiation incident on this surface is 5V. The incident radiation lies in

A. ultra-violet region
B. infra-red region
C. visible region  
D. X-ray region
Answer» B. infra-red region
2789.

In an experiment on photoelectric effect, a student plots stopping potential \[{{V}_{0}}\] against reciprocal of the wavelength \[\lambda \] of the incident light for two different metal A and B. These are shown in the figure. Looking at the graphs, you can most appropriately say that:

A. Work function of metal B is greater than that of metal A
B. For light of certain wavelength falling on both metal, maximum kinetic energy of electrons emitted from A will be greater than those emitted from B.
C. Work function of metal A is greater than that of metal B
D. Students data is not correct
Answer» E.
2790.

At t=0, light of intensity \[{{10}^{12}}\]\[{{10}^{12}}photons/s-{{m}^{2}}\]of energy 6eV per photon start falling on a plate with work function 2.5eV. If area of the plate is \[2\times {{10}^{-4}}{{m}^{2}}\]and for every \[{{10}^{5}}\]photos one photoelectron is emitted, charge on the plate at \[t=25s\] is

A. \[8\times {{10}^{-15}}C\]
B. \[4\times {{10}^{-14}}C\]
C. \[12\times {{10}^{-14}}C\]
D. \[16\times {{10}^{-14}}C\]
Answer» B. \[4\times {{10}^{-14}}C\]
2791.

Light coming from a discharge tube filled with hydrogen falls on the cathode of the photoelectric cell. The work function of the surface of cathode is 4eV. Which of the following values of the anode voltage (in volts) with respect to the cathode will likely to make the photo current zero?

A. -4
B. -6
C. -8
D. -10
Answer» E.
2792.

The work function for sodium surface is 2.0 eV and that for aluminum surface is 4.2 eV. The two metal are Illuminated with appropriate radiation so as to cause photoemission. Then

A. the threshold frequency for sodium will be less than that for aluminum  
B. the threshold frequency for sodium will be more than that of aluminum
C. both sodium and aluminum will have the same threshold frequency  
D. none of the above
Answer» B. the threshold frequency for sodium will be more than that of aluminum
2793.

A beam of light has two wavelengths of \[\text{4972}\overset{\text{o}}{\mathop{\text{A}}}\,\] and \[6216\overset{\text{o}}{\mathop{\text{A}}}\,\] with a total intensity of \[3.6\times {{10}^{-3}}W{{m}^{-2}}\] equally distributed among the two wavelengths. The beam falls normally on an area of \[1c{{m}^{2}}\] of a clean metallic surface of work function 2.3eV. Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photoelectrons liberated in 2s is approximately.

A. \[6\times {{10}^{11}}\]
B. \[9\times {{10}^{11}}\]
C. \[11\times {{10}^{11}}\]
D. \[15\times {{10}^{11}}\]
Answer» C. \[11\times {{10}^{11}}\]
2794.

Light of wavelength \[\text{200 }\overset{\text{o}}{\mathop{\text{A}}}\,\] fall on aluminum surface. Work function of aluminum is 4.2 eV. What is the kinetic energy of the fastest emitted photoelectrons?

A. 2eV      
B. 1eV
C. 4eV
D. 0.2eV
Answer» B. 1eV
2795.

When a metallic surface is illuminated with radiation of wavelength \[\lambda \], the stopping potential is V. If the same surface is illuminated with radiation of wavelength \[2\lambda \] the stopping potential is \[\frac{V}{4}.\]The threshold wavelength for the metallic surface is:

A. \[4\lambda \]     
B. \[5\lambda \]
C. \[\frac{5}{2}\lambda \]
D. \[3\lambda \]
Answer» E.
2796.

In the photoelectric experiment, if we use a monochromatic light, the I-V curve is as shown. If work function of the metal is 2eV, estimate the power of light used. (Assume efficiency of photo emission \[{{10}^{-3}}%\], i.e., number of photoelectrons emitted are \[{{10}^{-3}}%\]of number of photons incident on metal)      

A. 2W
B. 5W
C. 7W
D. 10W
Answer» D. 10W
2797.

Radiation of two photon energies twice and five times the work function of metal are incident successively on the metal surface. The ratio of the maximum velocity of photoelectrons emitted is the two cases will be

A. 1 : 2 
B. 2 : 1   
C. 0.0444444444444444
D. 0.167361111111111
Answer» B. 2 : 1   
2798.

Photoelectrons are ejected from a metal when light of frequency \[\nu \] falls on it. Pick out the wrong statement from the following.

A. No electrons are emitted if \[\nu \] is less than Wl h, -where W is the work function of the metal
B. The ejection of the photoelectrons is instantaneous.
C. The maximum energy of the photoelectrons is hi).
D. The maximum energy of the photoelectrons is independent of the intensity of the light.
Answer» D. The maximum energy of the photoelectrons is independent of the intensity of the light.
2799.

Find the number of photon emitted per second by a 25 watt source of monochromatic light of wavelength \[\text{6600 }\overset{\text{o}}{\mathop{\text{A}}}\,\text{.}\]  What is the photoelectric current assuming 3% efficiency for photoelectric effect?

A. \[\frac{25}{3}\times {{10}^{19}}J,0.4amp\]
B. \[\frac{25}{4}\times {{10}^{19}}J,6.2amp\]
C. \[\frac{25}{2}\times {{10}^{19}}J,6.2amp\]
D. None of these
Answer» B. \[\frac{25}{4}\times {{10}^{19}}J,6.2amp\]
2800.

If an electron is accelerated through a potential difference 150 volt, its de-Broglie wavelength is:

A. \[\text{1}\overset{\text{o}}{\mathop{\text{A}}}\,\]
B. \[\text{100}\overset{\text{o}}{\mathop{\text{A}}}\,\]
C. \[\text{5000}\overset{\text{o}}{\mathop{\text{A}}}\,\]
D. \[\text{90000}\overset{\text{o}}{\mathop{\text{A}}}\,\]
Answer» B. \[\text{100}\overset{\text{o}}{\mathop{\text{A}}}\,\]