Problem on Bohr atom model

Question:
A particle of charge equal to that of electron and mass 208 times the mass of electron (-meson)moves in a circular orbit around a nucleus of charge +3e (assume mass of nucleus to be infinite). Assuming that the Bohr atom model is applicable to this system
(a) derive an expression for the radius of the nth Bohr orbit
(b) find the value of n for which the radius of the orbit is approximately the same as that of the first Bohr orbit for the hydrogen atom
(c) find the wavelength of the radiation emitted when  -meson jumps from the third orbit to the first orbit (Rydberg constant = 1.097 x 107 m-1)  

Solution:

For solution click this link

IITJEE physics questions

Question 1
A glass of soft drink with ice cubes floating on it is taken to an elevator which is accelerating in downwards direction. Then portion of ice inside softdrink
(a) increases
(b) decreases
(c) remains same
(d) depends on the density of soft drink

Question 2
A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2:2:1. THe fragments having equal masses fly off along mutuall perpandicular directions with speed v. What will be the speed of the third fragment.
(a) v
(b)√v
(c) 2√2 v
(d) 3√2 v

Question 3
If a particle moving in a magnetic field , increases its velocity, then its radius of magnetic field energy will

(a) remain constant
(b) decrease
(c) increase
(d) either b or c


Question 4
A particle of charge q and mass m moves in a circular orbit of radius r with angular speed ω. The ratio of magnitude of its magnetic moment to that of its angular momentum depends on

(a) q and m
(b) ω , m and q
(c) ω and q
(d) ω and m


Question 5
Two coils are placed close to each other. The mutual induction of the pair of coils depends upon

(a) rates at which currents are changing in the coil
(b) relative position and orientation of two coils
(c) the material of the wires of the coil
(d) the currents in the two coils


Question 6
An eye specialist prescribed spectacles having an combination of convex lens of focal length 40 cm in contact with a concave lens of focal length 25 cm . The power of this combination in diopters is

(a) +1.5
(b) -1.5
(c) +6.67
(d) -6.67


Question 7
To observe the phenomenon of interference, we need tow sources emitting light of

(a) nearly same frequency
(b) the same frequency
(c) different wavelengths
(d) same frequency and having definite phase relationship


Answers
1. c
2. c
3. c

4. a
5. b Mutual inductance of pair of coils depends on relative position and orientation of the two coils. This is in addition to other factors not given in the alternatives.
6. b use P=P₁+P₂ where p is total power of combination of lenses
7. d

IITJEE previous year questions

Question 1
A particle executes SHM with frequency f. The frequency with which its Kinetic energy oscillates is
(a) f/2
(b) f
(c) 2f
(d) 4f

Question 2
A linear harmonic oscillator of force constant 2 x 10⁶N/m and amplitude 0.01 m has a total mechanical energy of 160J. Its
(a) Maximum potential energy is 100J
(b) Maximum kinetic energy is 100J
(c) Maximum potential energy is 160J
(d) Minimum potential energy is zero

Question 3
A given quantity of ideal gas is at pressure P and absolute temperature T. The isothermal bulk modulus of gas is
(a) 2P/3
(b) P
(c) 3P/2
(d) 2P

Question 4
During the melting of slab of ice at 273K at atmospheric pressure
(a) positive work is done by the ice water system on the atmosphere
(b) positive work is done on the ice water system by the atmosphere
(c) the internal energy of the ice water system increases
(d) the internal energy of the ice water system decreases


Question 5
When an ideal diatomic gas is heated at a constant pressure , the fraction of the heat energy supplied which increases the internal energy of the gas is
(a) 2/5
(b) 3/5
(c) 3/7
(d) 5/7
 
Question 6
In a given process on an ideal gas , dW=0 and dQ<0. then for the gas
(a) the temperature will decrease
(b) the volume will increase
(c) the pressure will remain constant
(d) the temperature will increase

Question 7
A cylinder rolls up an inclined plane, reaches some hight, and then rolls down (without slipping through these motions). The directions of frictional force acting on the cylinder are
(a) up the incline while ascending and down the incline descending
(b) up the incline while ascending as well as descending
(c) down the incline while ascending and up the incline while descending
(d) down the incline while ascending as well as descending
 
 

Answer
1. c
2. c,d
3. b
4. b,c
5. d
6. a
7. b

Objective Type questions : Test Yourself

1. A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to
(a) x²
(b) e^x
(c) x
(d) log_e x

2. Which of the following statements is false for a particle moving in a circle with a constant angular speed.
(a) The velocity vector is tangent to the circle
(b) the acceleration vector is tangent to the circle
(c) the acceleration vector points to the centre of the circle
(d) the velocity and acceleration vectors are perpandicular to each other

3. If A × B = B × A, then angle between both the vectors is
(a) π
(b) π/3
(c) π/2
(d) π/4

4. A ball is released from top of the tower of hight h m. It takes t sec. to reach the ground. What is the position of ball in T/3 sec.
(a) h/9 m from the ground
(b) 7h/9 m from the ground
(c) 8h/9 m from the ground
(d) 17h/18 m from the ground

5. A machine gun fires a bullet of mass 40g with a velocity 1200 m/s. the man holding it can exert a maximum force 144 N on the gun. How many bullets can he fire per second at the most.
(a) one
(b) four
(c) two
(d) three

Answer
1. a
2. b
3. a
4. c
5. d

Test Yourself (Miscellaneous MCQ's)

Qiestion 1
If relatibe permeability of iron is 5500 then its magnetic susceptibility is
(a) 5500 x 10⁷
(b) 5501
(c) 5499
(d) 5500 x 10^-7

Question 2
An atom is paramagnetic if it has
(a) an electric dipole moment
(b) no magnetic moment
(c) a magnetic moment
(d) no electric dipole moment

Question 3
Magnetic moment of a diamegnetic atim is
(a) 0
(b) infinity
(c) negative
(d) positive

Question 4
Mark the correct statement(s)
(a) When a particle moves under uniform circular motion its acceleration is constant
(b) Under the influence of uniform circular motion , instantaneous acceleration is perpandicular to the tangential velocity
(c) Under the influence of non-uniform circular motion , instantaneous acceleration is perpandicular to the tangential velocity
(d) All the above

Qiestion 5
In a meter bridge apparatus , the bridge wire should have
(a) high resistivity and low temperature coefficent
(b) high resistivity and high temperature coefficent
(c) low resistivity and high temperature coefficent
(d) low resistivity and low temperature coefficent

Question 6
Mark out the correct statement
(a) Image formed by convex mirror can be real
(b) Image formed by convex mirror can be virtual
(c) Image formed by convex mirror can be magnified
(d) Image formed by convex mirror can be inverted

Answer
1. c
2. c
3. a
4. b .... When a particle moves under the influence of uniform circular motion magnitude of acceleration is always constant but direction of acceleration keeps changing, it always remains towards the centre . So acceleration is always perpandicular to the the tangential velocity in this case.
5. a
6. a,b,c,d

IITJEE/AIEEE test series links

hi all
Whether you are preparing for competetive exams like IITJEE/PMT/AIEEE or you are looking for some serious knowledge in physics you need to check your knowledge time to time so that you are aware of the preperation you have done . So here I am giving you the links for IITJEE/AIEEE test series in physics.Those who are not preparing for such exams can also take the test to check their knowledge. Hope they help you. So take a test of your knowledge in physics
Test series 1
Test series 2
Test series 3
Test series 4
There are three other test series available on general topics in physics for those you would have to register yourself to the
website

for further information contact mailmephysics12@rediffmail.com.

Physics questions for IITJEE, AIEEE, PMT preperation

Given below are the questions you can prepare for IITJEE-2011, AIEEE-2011 and PMT-2011 examinations. Few questions from the questions given below have been aske in previous year IITJEE, AIEEE and other such exams.

Question 1. Three capacitors of 8μF , 12μF and 24μF are connected (A) in series combination and then (B) in parallel combination . The ratio of equivalent capacitance in case (B) to that of case (A) is
(a) 11:1
(b) 1:11
(c) 1:1
(d) 3:1

Question 2. A piece of copper and a piece of germanium are cooled from the room temperature down to 80K
(a) resistance of each of them increases
(b) resistance of each of them decreases
(c) resistance of copper increases and that of germanium drcresaes.
(d) resistance of copper decreases and that of germanium increases.

Question 3. A current flows along the length of infinitely -long straight , thin walled pipe then,
(a) magnetic field at all points inside the pipe is same , but non zero
(b) the magnetic field at any point inside the pipe is zero.
(c) magnetic field is zero only on the axis of the pipe
(d) magnetic field is different at different points inside the pipe

Question 4. The line on the earth's surface joining the points where the field is horizontal is called
(a) magnetic maredian
(b) magnetic axis
(c) isogonic line
(d) magnetic equator

Question 5. The principle used in the transmission of signal through an optical fibre is
(a) total internal reflection
(b) reflection
(c) refraction
(d) dispersion

Question 6. Milikan's oil drop experiment established that
(a) electric charge depends on velocity
(b) electron has wave nature
(c) electron has particle nature
(d) electronic charge is quantized

Question 7. For steady direct current to flow in a circuit
(a) circuit must contain a source of emf
(b) charge distribution in circuit must remain unchanged
(c) lines of current density vector are closed one
(d) all of the above

I hope that these question answes will help you prepare physics for IITJEE, AIEEE and PMT exams

Answer:-
1. (a)
2. (d)
3. (b)
4. (d)
5. (a)
6. (d)
7. (d)

Thermodynamics Questions along with solutions (Questions for IITJEE)

Question 1:A gas is contained in a vertical, frictionless piston cylinder device. The piston has a mass of 20 kg with a cross-sectional area of 20 cm² and is pulled with a force of 100N. If the atmospheric pressure is 100 kPa, determine the pressure inside.


Question 2:A piston-cylinder device has a ring to limit the expansion stroke. Initially the mass of Oxygen is 2 kg at 500 kPa, 30° C. Heat is now transferred until the piston touches the stop, at which point the volume is twice the original volume. More heat is transferred until the pressure inside also doubles. Determine the amount of heat transfer and the final temperature.


Question 3: A piston cylinder device contains 1 kg of oxygen at 150 kPa, 30°C. The cross-sectional area of the piston is 0.1 m². Heat is now added causing gas to expand. When the volume reaches 0.2 m³, the piston reaches a linear spring with a spring constant of 120 kN/m. More heat is added until the piston rises another 25 cm. Determine the final pressure, temperature and the energy transfers.


Question 4:Is the energy of the system U an intensive or extensive variable?



Question 5:Suppose we have M+N systems prepared, and the first is in thermal equilibrium with the second, the second in thermal equilibrium with the third, etc., until system M+N- 1 is in thermal equilibrium with the M+Nth system. Is the first system in thermal equilibrium with the M+Nth?


Question 6:A gas is contained in a cylinder with a moveable piston on which a heavy block is placed. Suppose the region outside the chamber is evacuated and the total mass of the block and the movable piston is 102 kg. When 2140 J of heat flows into the gas, the internal energy of the gas increases by 1580 J. What is the distance s through which the piston rises?


Question 7:A resistance thermometer is such that resistance varies with temperature as
R_T=R₀(1+aT+bT⁵)
where T represent Temperature on Celsius scale And a,b,R₀ are constants.R₀ unit is ohm
Based on above data ,Find out the unit of a,b


Solutions

Please take a look at other Thermal post
Thermal Expansion
Study Tips Part 1
Study Tips Part 2
Thermo Quick Recap
Conceptual Questions Part 1
Conceptual Questions Part 2
Conceptual Questions Part 3
Conceptual Questions Part 4
IITJEE Objective Questions part 1
IITJEE Objective Questions Part 2
Thermal Expansion Problems
IITJEE Subjective Questions
Thermo Questions

Gravitation questions for IITJEE

1.Which is of the following statement is true
A) Gravitational constant G value does not depend on the medium between the bodies
B) Gravitational constant G depends on the masses of the bodies and the sizes of the bodies
a A & B both are correct
b only A is correct
c Only B is correcr
d A and B both are wrong

2.If the distance between the earth and sun were half its present value,the number of days in a year would be
a. 64.5
b. 129
c. 182.5
d. 730

3.if both the mass of earth and its radius are decreased by 1%,the value of acceleration of gravity will
a. Decrease by 1%
b Increase by 1%
c. Increase by 2%
d remain unchanged

4. A body weigh W newton of the surface of the earth.Its weight at a height equal to half the radius of the earth will be
a. W/2
b. 2W/3
c. 4W/9
d. W/4

5.when a stone of mass m is falling in th earth of mass M,the acceleration of the earth will be
a zero
b. mg/M
c. Mg/m
d g

6.The weight of the object will be
a. zero at the center of the earth
b.same in all the satellites
c. same at all the points on the surface of the earth
d. none of the above

7.Which is of the following statement is true
A) it is possible to put an artificial satellite in a orbit such a way that it will remain always directly over New Delhi
B) An earth satellite continues to move in the orbit due to centripetal force provided by the burning of the fuel of its engine
a A & B both are correct
b only A is correct
c Only B is correcr
d A and B both are wrong


8. A mass m is divided into two part ym and (1-y)m .For a given seperation,the value of y for which the gravitattional attraction between the two pieces becomes maximum
a. 1/2
b. 3/5
c. 1
d 2

9.Two bodies of mass M and 2M are at rest at infinte seperation.They move towards each other under the mutual gravitaional attraction.Then at seperation r ,which of the following is false
a. The total energy of the system is not zero
b The force between them is zero
c. The center of the mass of the system is movind
d non of the above

10.Choose the correct statement
a. the gravitational forces between the two bodies are an action and reaction pair
b. G and g are constant everywhere
c.The acceleration due to gravity increase due to rotation of the earth
d. none of the above


Solutions

Current electricity test series

(A) Assertion reason type question.

(a) If both assertion and reason are true and reason is correct explaination of assertion.
(b) If both assertion and reason are true and reason is not correct explaination of assertion.
(c) Assertion is true but reason is false.
(d) both assertion and reason are false.

(1)
Assertion:Wire carrying current is not charged.
Reason:It is because , at any instant number of electrons leaving wire is sometimes equal to the number of electrons flowing in from the battery.


(2)
Assertion:Drift velocity of electrons decreases on increasing temperature of the conductor.
Reason:It is because, on increasing temperature of a conductor , the value of resistivity of it's material increases.


(3)
Assertion:Resistors are connected in series combination in order to increase the resistance of the circuit.
Reason:In series combination potential difference across any resistor is proportional to it's resistance.


(4)
Assertion:A potentiometer measures the potential difference more accurately then a voltmeter.
Reason:Because it has a wire of high resistance and draws a heavy current from external circuit.


(B) Multiple choice questions with only one answer

(5) A constant voltage is applied between the two ends of a uniform metalic wire and some heat is developed in it . The heat developed is doubled if,
(a) both length and radius of wire are halved
(b) both length and radius of wire are doubled
(c) radius of wire is doubled
(d) length of wire is doubled


(6) Kirchoff's first law of electric circuits is based on the law of conservation of
(a) only on mass
(b) only on charge
(c) on charge as well as on energy
(d) on charge as well as on mass


(7)The temperature coefficent of resistance of wire is 0.00125°C^-1. At 300K, it's resistance is 1 ohm. The resistance of wire would be 2 ohm at
(a) 1154K
(b) 1127K
(c) 1167K
(d) 1176K


(8) If the length of the potentiometer wire is increased, then the accuracy in determination of null point
(a) will increase
(b) will decrease
(c) will remain unaffected
(d) can not be decided , untill emf of auxiliary battery is known


(9) Each of the resistance in the network shown in the figure is equal to R. The resistance between terminal A and B is


(a) R
(b) 5R
(c) 3R
(d) 6R




(10)The current voltage graph for a given metallic wire at two different temperatures T₁ and T₂ are shown in the fig. which one of the following option is true


(a) T₁ = T₂
(b) T₁ < T₂
(c) T₁ > T₂
(d) none of the above



Solutions
1.c
2.a
3.b
4.c
5.b
6.b
7.b
8.a
9.a
10.b

IITJEE Testseries Thermodynamics -I

Mulitiple Choice questions with Single answer
1. A rod of length L having coefficent of Linear expansion α is lying freely on the floor.it is heated so that temperature changes by ΔT .Find the longitidunal strain developed in the rod
a. 0
b. αΔT
c. -αΔT
d. none of the above

2.if a is coefficent of Linear expansion,b coefficent of areal expansion,c coefficent of Volume expansion.Which of the following is true
a. b=2a
b. c=3a
c. b=3a
d. a=2b

3. There are two statement
A. Equal volumes of all gases at the same temperature T and pressure P contain an equal no of Molecules
B.the no of molecules in one mole of any gas is 6.0255 * 10²².
which one of the following is correct
a. A and B both
b. A only
c B only
d. A and B both are incorrect

4.There are two statement about Ideal gases
A. The V_rms of gas molecules depends on the mass of the gas molecule and the temperature
B. The V_rms is same for all the gases at the same temperature
which one of the following is correct
a. A and B both
b. A only
c B only
d. A and B both are incorrect

5. Consider the following two statement
A.If heat is added to the system,it temperature must increase
B.If dW >0 then dV >0
a A & B both are correct
b A is correct only
c. B is correct only
d A &B both are wrong

Mulitiple Choice questions with More than one answer
6.which of the following is correct
a. Molar heat capacity is 0 for PV^y=Constant
b. Molar heat capacity is infinity in adiabatic process
c. Internal energy does not change in Isothermal Process
d. All the above

7.An ideal gas is taken from state A(P₁,V₁) to state B(P₂,V₂) by two method X & Y..which of the following is correct
a.ΔQ₁-ΔW₁=ΔQ₂-ΔW₂
b.ΔU₁=ΔU₂
c. ΔQ₁+ΔW₁=ΔQ₂+ΔW₂
d. None of the above

8 what is true for black body
a e=a=1
b emit radiation and absorb radiation
c. refract radiation
d none of the above

Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True
9. STATEMENT 1:The molar specfic heat capacity of the ideal gas in adiabatic process is zero
STATEMENT 2: Heat transfer is zero in the adiabatic process

10.STATEMENT 1:The internal energy between two state is independent of the process path
STATEMENT 2: Internal enerby is intrinsic property of the system

11.STATEMENT 1:Gases behave like ideal gas at high temperature
STATEMENT 2:Intermolecular forces are neglibible at high temperature



Matrix Match type
12. A gas has five molecules having velocities v,2v,3v,4v,5v.Match the column I to column II
column I
P. (V_rms)²
Q. (V_mean)²
R (V²)_mean
S. (V²)_mean - (V_rms)²

column II
W. 9v²
X. 11v²
Y. 10v²
Z. 0

13. Match the column I to column II
column I
P Adiabatic expansion
Q Isothermal compression
C Constant Presure expansion
D.Constant Volume with increase in pressure

column II
W. ΔW>0
X. ΔQ>0
Y. ΔW<0
Z. ΔQ<0

Linked Comphrension type
A cylindrical vessel with its axis vertical,contains one mole of a molecular gas at
thermodynamic equilibrium.The upper base of the cylinder can be displaced freely.It is made of glass plate.Atmospheric pressure is P₀ and Temperature of the gas is T₀.mass of the glass plate is m.There is no heat transfer through the wall of the vessel.The gas is heated through radiation through the glass plate for some time such that the upper plate gets displaced by Δh.The radius of the cylinder is r.Find the following

1. Final temperature of the gas when it get displaced by Δh
a.T₀ +Δh(P₀πr²+mg)/R
b.T₀ -Δh(P₀πr²+mg)/R
c. Δh(P₀πr²+mg)/R
d. None of the above

2. Find out the workdone by the gas
a.Δh(P₀πr²+mg)
b.mgΔh
c. Δh(P₀πr²-mg)
d. none of the above


3.Find the total heat gained by the gas
a.Δh(P₀πr²+mg)(C_V/R +1)
b.Δh(P₀πr²-mg)(C_V/R +1)
c.Δhmg(C_V/R +1)
d.none of the above

IITJEE Test Series for SHM

Mulitiple choice questions with one answer

1.The amplitutde and phase of a particle executing SHM depends on
a.The displacemnt of particle at t=0
b.The velocity of particle at t=0
c Both Velocity and displacement at t=0
d Neither velocity and displacemnt at t=0


2.A particle of mass m is attached to a massless string of lenght L and is oscillating in vertical plane with one end of string fixed to rigid support.Tension in the string at a certain instant is T=kmg.Then
a. K can never be equal to 1
b. K can never be greater than 1
c. K can never be greater than 3
d K can never be less than 1

3. A particle is executing SHM at mid point of mean position and extreme position . What is it's KE in terms of total energy E.

(a) E/2
(b) 4E/3
(c) √ 2E
(d) 3E/4

4. A spring of force constant k is cut into two pieces such that one piece is four times the length of the other. the longer piece will have force constant equal to

(a) 4k/5
(b) 5k/4
(c) 3k/2
(d) 4k

5. Total energy of mass spring system in harmonic motion is E=1/2(mω²A²). Consider another system executing SHM with same amplitude having value of spring constant as half the previous one and mass twice as that of previous one. The energy of second oscillator will be

(a) E
(b) 2E
(c) √ 2E
(d) E/2

Mulitiple choice questions with more then one answer

6.For a particle executing SHM
a.Acceleration is proportional to the displacement in the direction of the motion
b.Acceleration is proportional to the displacement but in opposite direction of the motion
c. Total energy of particle remains constant
d KE and PE of particle remains constant


7. which one of the following statement is true
a. Maximum value of velocity in SHM is A²ω
b.In SHM velocity of the particle is maximum when displacment is maximum
c.Velocity of the particle is zero in SHM when displacement attains its maximum on either side
d.Velocity in SHM vary periodically with time


8. which one of the following statement is true
a. Amplitude and intial displacement of particle in SHM are always equal
b.Amplitude and intial displacement of particle in SHM are never equal
c. Amplitnude of a particle in SHM can be equal to its initial displacement
d. Amplitnude of a particle in SHM can be greater to its initial displacement


9.To execute SHM system must have
a. Elasticity
b. Moment of Inertia
c. Inertia
d. all the above


10. Angular frequency of system executing SHM depends on
a. mass
b. total energy
c.force constant
d. Amplitude


Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True

11.
STATEMENT 1:Frequency of oscillation in Simple pendulum depends on Amplitude of oscillation
STATEMENT 2:Timeperiod of oscillation in simple pendulum is given by T=2π√L/g

12.
STATEMENT 1:Total energy remains constant in SHM
STATEMENT 2:KE is maximum at mean position

13.
STATEMENT 1:The quantity F.r where F is force and r is displacement is negative in SHM
STATEMENT 2:THe quantity a.r where a is acceleration and r is displacement is positive in SHM

14.
STATEMENT 1:The amplitude or energy is defined by the intial position and intial velocity in SHM
STATEMENT 2:THe phase of motion is determined by the intial position and intial velocity in SHM

MAtrix match type

15.
In a spring mass system executing SHM having mass m and spring constant K with Timeperiod T.Match the column I to the column II

Column I
A) Amplitude is doubled
B) Mass is doubled
C) Spring constant is doubled and mass is 2 doubled also
D)Amplitude is doubled and spring constant is made half

Column II
A) Timeperiod is T
B) Timeperiod is T√2
C) Timeperiod is 2T
D) no match is appropiate


Linked Comphrehension Type
A block of mass M₁ resting on the frictionless surface is connected to a spring of spring constant K that is anchored in the nearby wall.A block of mass M₂=aM₁ is placed on the top of the first block.The coefficent of static friction between the two bodies is μ_s

16 Assuming the two bodies moves as single object,find the period of oscillation of the system
a T=2π√(1+a)M₁/k
b T=2π√M₁/k
c. T=2π√(1-a)M₁/k
d. None of the above

17. Find the maximum oscillation magnitude A_max that permits the two bodies to move as unit
a. A_max=(1+a)μ_sgM₁/k
b. A_max=μ_sgM₁/k
c. A_max=μ_sgM₂/k
d. none of the above

18.find the maximum static frictional force on the body M₂
a. μ_sgM₁
b. μ_sgM₂
c. μ_sgaM₁
d. none of the above

Solutions

IIT JEE Test Series(Electricity-1)

Multiple choice question with only one answer

1.A rod lies along the x-axis with one end at the origin and other at x->∞it caries a uniform charge λ C/m.Find the electric field at the point x=-a on the x-axis
a. -(λ/4πε₀a)i
b.-(λ/4πε₀a²)i
c. (λ/4πε₀a)i
d. (λ/4πε₀a²)i


2.Twelve charges of charge q are situated at the corners of the 12 sided polygon of side a.What is the net force on the charge Q at the center
a. Zero
b. 3qQ/πε₀a²
c. qQ/πε₀a²
d None of the above



3.Two positive point charge are placed at the distance a apart have sum Q.What values of the charges,coulumb force between them is maximum
a.q₁=q₁=Q/2
b. q₁=3Q/4 ,q₂=Q/4
c. q₁=5Q/6 ,q₂=Q/6
d Non of the above


4.A metallic shell having inner radius R₁ and outer radii R₂ has a point charge Q kept inside the cavity.Electric field in the region R₁ < r < R₂ where r is the distance from the center is given by
a depends on the value of r
b zero
c, Constant and nonzero everywhere
d. None of the above


5.Consider two statements
A)The force with which two charges interact is not changed by the presence of the other charges
B)Electric force expierenced by the charge particle due to number of fixed point charges is vector resultant of the forces expierence due to individual charges
a) A and B both are correct
b) A is correct only
c) B is correct only
d. A and B both are wrong

Multiple choice question with more than one answer

6)A metallic sold sphere of radius R is given the charge Q.Which of the following statement is true then
a) Electric field at points 0< r < R is zero
b) Charge Q is on the outer surface of the sphere
c) Electric field at r>R is given by Q/4πε₀r²
d) Electric field is perpendicular to the surface of the sphere



7)A simple pendulum consists of a small sphere of mass and posutive charge q is suspended by the string of length L.The pendulum is placed in the electric field of strength E directed vertically downwards.Which of the following is true
a)Time period of oscillation=T=2π√L/(g+qE/m)
b)Time period of oscillation=T=2π√L/(g-qE/m)
c) Tension in the string when the pendulum is at rest =mq+qE
d)Tension in the string when the pendulum is at rest =mq-qE


8)A rod lies on the x-axis with end end at x=-L and other end at x=L with uniform charge λ C/m.Which of the following is true
a.Electric field at any point (0,y) on the y-axis is given by
E=(2kλL/y√(y²+L²))j
b. For point on the Y-axis greater than y>>>>L
E=(2kλL/y²)j
c. Electric field if L->∞
E=2kλ/y
d. None of the above


9. A particle of mass m and charge q is thrown horizontally with a velocity v from top of the building of height H.An electric field exists in the plane and it is horizontally away from the building
which of the following is true
a) Range of the particle is greater than v√(2H/g)
b) Time of flight is √(2H/g)
c) Path is parabolic
d None of the above



Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True

10.
STATEMENT I:There is no electric field in conducter in electrostatics
STATEMENT II:There are plenty of free electron in the conductor which moves in such a way to cancel all the electric field



11.
STATEMENT I:Coulumb law of forces are a action reaction pair
STATEMENT II:Coulumb law of forces are non conservative in nature



12.
STATEMENT I:Two electric lines of forces never intersect
STATEMENT II:Electric lines of forces originate from -ve charge and terminate on +ve charge



13.
STATEMENT I:Excess charge given to conductor always reside on the outer surface
STATEMENT II:E is zero inside the bulk material of the conductor


Matrix Match type
14) A metallic shell is having a charge q at the center.Column I gives the location of the charge,Column II defines the charge distribution on the surface due to the charge.You have to match the statement in Column I to column II

Column I
A) q is at the center
B) q is displaced from the center
C) An excess charge Q is given to the metallic shell
D) An Charge Q is placed near the shell

Column II
P)Charge distribution is uniform at the inner surface of the metallic shell
Q)Charge distribution is non uniform at the inner surface of the metallic shell
R)Charge distribution is uniform at the outer surface of the metallic shell
S)Charge distribution is non uniform at the outer surface of the metallic shell


Linked Comprehension Type

A electric charge q of mass m is projected horizontally with a velocity v in the Uniform elctric field which occupies limited space in the region.Electric field E is vertically upwards.And the limited region of the electric field is of length a.Assuming X axis as horizontal and Y-axis as vertical.And let us assumes charge start from origin in the electric field.
Answer following question based on this

15)Horizontal components and Vertical components of the velocity when it passes through the end of the field i.e at x=a
a)v,qEa/mv
b)v,qE/mv
c)qEa/mv,a
d)qE/mv,v


16) Equation of the motion of the particle
a) staright line
b) parabola
c) circle
d) none of the above



17) if the charge get deflected by angle α when it comes out of electric field ,then which one is true
a) tanα=qEa/mv²
b) tanα=qEa/mv
c) sinα=qEa/mv
d) sinα=qEa/mv²


Solutions