the effective resistance between points p and q of the ... · the effective resistance between...

MEE-2016 Physics

Explained By: Rajesh Tripathy Sir.

1. The effective resistance between points P and Q of the electrical

circuit shown in the following figure is

Ans= (a) hint:- use balanced wheatsone bridge condition

2. A constant voltage is applied between the two ends of a uniform

metallic wire. Some heat is developed in it. The heat developed is

doubled if

Ans= (b)

3. Two particles A and B having equal charges, after being

accelerated through the same potential difference, enter a region

of uniform magnetic field and describe circular paths of radii 𝑅1

and 𝑅2 respectively. The ratio of mass A to the mass of B is

Ans= (c) hint:- use r=mv/qB and q= 2𝑞𝑉/𝑚

4. An alternating voltage (in volts) given by V=200 2 sin (100t) is

connected to 1 𝜇F capacitor through an a.c. ammeter. The

reading of the ammeter will be V=200 2 sin (100t)

Ans= (c)

5. In the visible region, the dispersive powers and the mean angular

deviations for crown and flint glass prisms are 𝜔 and 𝜔′, and 𝑑

and 𝑑′ respectively. When the two prisms are combined, the

condition of zero dispersion by the combination is

Ans= (c)

6. If two waves of intensities 𝐼 and 4𝐼 superpose, then the

maximum and minimum intensities are

Ans= (b) hint:- use( 𝐼1+ 𝐼2)2

( 𝐼1− 𝐼2)2

7. The wavelength of 𝐾𝛼 line from an element of atomic number 41

is λ. Then the wavelength of 𝐾𝛼 line of an element of atomic

number 21 is

MEE-2016 Physics


Ans= (a)

8. Which of the following is not true?

The half-life of a radioactive substance does not depend on

Ans= (c)

9. A student measures the value of g with the help of a simple

pendulum using the formula g=4𝜋2𝐿

𝑇2 . The errors in measurements

of L and T are ∆𝐿 and ∆𝑇 respectively. In which of the following

cases is the error in the value of g the minimum?

Ans= (d)

10. A particle moving in a straight line covers half the distance

with a speed of 3 m/s. The other half of the distance is covered in

two equal time intervals with speeds of 4.5 m/s and 7.5 m/s

respectively. The average speed of the particle during the motion

is

Ans= (a) hint:- use average voltage=𝑇𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑇𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒

11. A projectile has the same range R when the maximum height

attained by it is either ℎ1 or ℎ2. Then R, ℎ1 and ℎ2 will be related

as

Ans= (d)

12. The maximum height attained by a projectile is increased by

10% by changing the angle of projection, without changing the

speed of projection. The percentage increase in the time of flight

will be

Ans= (d)

13. A particle moves in the 𝑥-𝑦 plane under the influence of a

force such that its linear momentum is →

𝑃 (t) = A[î cos 𝐾𝑡 −

MEE-2016 Physics


ĵ sin(𝐾𝑡)], where A and K are constants. The angle between the

force and momentum is

Ans= (a) hint:- use F=𝑑𝑝

𝑑𝑡 if →

𝐹. →𝑃

= 𝑂 then "𝐹 ⊥𝑟𝑝

14. In which of the following, work is done by the force?

Ans= (d)

15. A body falls from a height h on a horizontal surface and

rebounds. Then it falls again and again rebounds and so on. If the

coefficient of restitution is 1

3, then the total distance covered by

the body before it come to rest is

Ans= (b)

16. A gramophone record of mass M and radius R is rotating at

an angular velocity 𝜔. A coin of mass m is gently placed on the

record at a distance r 𝑅

2 from its centre. The new angular velocity

of the system is

Ans= (a)

17. The escape velocity of a body on the earth’s surface is 𝑣𝑒 . A

body is thrown with a speed 3𝑣𝑒 . Assuming that the sun and

planets do not influence the motion of the body, its speed at

infinity would be

Ans= (d)

18. The volume of a wire remains unchanged when the wire is

subjected to a certain tension. The Poisson’s ratio of the material

of the wire is

Ans= (d)

19. Equal volumes of two substances of densities 𝜌1 and 𝜌2 are

mixed together. The density of the mixture would be

Ans= (a)

MEE-2016 Physics


20. The period of oscillation of a simple pendulum of length L

suspended from the roof of a vehicle which moves without

friction down an inclined plane of inclination α is given by

Ans= (a)

21. A policeman moving at 22 m𝑠−1 chases a motorcyclist. The

policeman sounds his horn at 176 Hz, while both of them move

towards a stationary siren of frequency 165 Hz. If the

motorcyclist does not observe any beats, his speed must be (take

speed of sound = 330 𝑚𝑠−1)

Ans= (b)

22. According to the theory of specific heat of solids at

extremely low temperature (close to absolute zero), the specific

heat S of a solid varies with absolute temperature T as

S=𝑐𝑇3

where c is a constant depending on the material of the solid. The

heat energy required to raise the temperature of 0.1 kg of the

solid from 0 K to 4 K is

Ans= (b) hint:- use Q=m 𝑠𝑑𝑡4

0

23. The P-V diagram for 2 moles of an ideal gas undergoing a

process A → B is shown in the figure below

The maximum temperature of the gas during the process is

Ans= (a)

24. Which of the following phenomena gives evidence of the

molecular structure of matter?

Ans= (b)

25. A electron of mass 𝑚𝑒 , initially at rest, moves through a

certain distance in a uniform electric field in time 𝑡1. A proton of

mass 𝑚𝑝 , also initially at rest, takes time 𝑡2 to move through an

MEE-2016 Physics


equal distance in this field. Neglecting the effect of gravity, the

ratio 𝑡2

𝑡1 is nearly equal to

Ans= (b) hint:- use 𝑆1 = 𝑆2 and 𝑎 =𝑞𝐸

𝑚

26. The magnetic field in a plane electromagnetic wave is given

by 𝐵𝑦 = 2 × 10−7 sin(0.5 × 103𝑥 + 1.5 × 1011𝑡) This

electromagnetic wave is

Ans= (c)

27. Assuming human pupil to have a radius of 0.25cm and a

comfortable viewing distance of 25cm, the minimum separation

between two objects that human eye can resolve at 500nm

wavelength is

Ans= (b)

28. A photoelectric surface is illuminated successively by

monochromatic light of wavelength λ and 𝜆

2. If the maximum

kinetic energy of the emitted photoelectrons in the second case

is 3 times that of the first case, the work function of the material

is

Ans= (b) hint:- use KE=ℎ𝑐⊼

− 𝜔0

29. If 𝑁𝑜 is the original mass of a substance of half=life period 5

years, then the amount of the substance left after 15 years is

Ans= (d) hint:- use N=𝑁0(1

2)𝑛

30. A p-type semiconductor has acceptor levels 57 millielectron

volt above the valence band. The maximum wavelength of light

required to create a hole is

Ans= (c)

31. The highest energy of the electron at absolute zero in a

metal is called

MEE-2016 Physics


Ans= (a)

32. The space waves which are affected seriously by

atmospheric conditions are

Ans= (b)

33. The length of a half-wave dipole at 30 MHz is

Ans= (c)

34. The energy of a light quantum can be expressed in the unit

of inverse length under the condition

Ans= (d)

35. The cosmic microwave background (CMB) radiation

resembles the spectrum of a blackbody at 2.7 K. The wavelength

at which the energy density of this blackbody radiation peaks is

Ans= (a)

36. An endoscope works on the principle of

Ans= (a)

37. A hare and a tortoise take part in a race of d metres. The

hare starts of quickly and gains an early lead over the tortoise

with accelerated motion. After some time, the hare looks behind

and finds the tortoise far behind. Hence, it stops to run and takes

a nap. Meanwhile, the tortoise keeps moving with uniform speed

with which it started. The tortoise makes slow but steady

progress crossing the sleeping hare and is about to reach the

destination. That is when the hare wakes up and shakenly starts

to run as fast as it can, again with accelerated motion. But all its

efforts go in vain and the tortoise reaches the destination first.

Which of the following graphs between distance 𝑥 and time t

correctly represents the above story? (Here, the line H represents

the hare and the line T represents the tortoise)

MEE-2016 Physics


Ans= (a)

38. A particle of mass m exhibits one-dimensional simple

harmonic motion with angular frequency 𝜔. The plot between

the linear momentum 𝑃 of the particle and its position multiplied

by m𝜔, 𝑚𝜔𝑥 at total energy E of the particle is shown below

The radius of the circle shown above is proportional to

Ans= (b) hint:- use E=1/2𝐾𝐴2 A× 𝐸1/2

39. Three charges are placed on the circumference of a circle of

radius R as shown in the figure below

The two charges Q subtend an angle 90° at the centre of the

circle. The charge q is placed symmetrically with respect to the

charges Q. If the electric field intensity at the centre is zero, what

is the magnitude of Q?

Ans= (a)

40. 10 g of ice at 0 ℃ is added to a beaker containing 10 g of

water at 70 ℃. What is the final temperature of the system when

it comes to thermal equilibrium?

(Specific heat of water=1 cal/g/ ℃

Latent heat of melting of ice = 80 cal/g)

Ans= (d) hint:- use principle of calori metry

41. Consider the position vectors of two particles →

𝑟1 and

→

𝑟2. They

make an angle 𝜃 between them. The ratio of the two vectors is

then given by

Ans= (d)

42. N particles are arranged along the positive N particles are

arranged along the positive 𝑥-axis of a coordinate system as

follows: The first particle of mass 1 kg is kept at a distance 1 m

along the 𝑥-axis from the origin, the second particle has mass 2

MEE-2016 Physics


kg and is kept at a distance of 2 m from the origin and so on, such

that the Nth particle has mass N kg and is kept at a distance of N

m. from the origin.

The distance (in metres) of the centre of mass from the origin

along the 𝑥-axis is

Ans= (b)

43. The energy from electromagnetic waves in equilibrium in a

cavity is used to melt ice. If the Kelvin temperature of the cavity

is increased by a factor of two, the mass of ice that can be melted

in a fixed amount of time is increased by a factor of

Ans= (d)

44. The displacement-time graph of a particle is shown below

The corresponding velocity-time graph will be

Ans= (a)

45. A man throws a ball A vertically upward with a speed 𝑢. At

the same time, another ball B is released from a height h. At time

t, the speed of A relative to B is

Ans= (a)

46. The angle of projection for which the horizontal range and

the maximum height are equal, is

Ans= (a) hint:- R=H

47. The ratio of acceleration due to gravity at a height h above

the surface of the earth and at a depth h below the surface of the

earth (for h ≪ radius of the earth R) is

Ans= (b)

48. The ratio of the energy required to raise a satellite up to a

height h above the earth of radius R to that of the kinetic energy

of the satellite in the orbit is

MEE-2016 Physics


Ans= (b)

49. 5 g of air is heated from 0 ℃ to 4 ℃ at constant volume. The

change in internal energy is (the specific heat of air at constant

volume is 0.172 cal 𝑔−1℃−1)

Ans= (b) hint:- ∆ ∪= 𝑛𝑐𝑣∆𝑇

50. A particle executes SHM of amplitude ±𝑎. The time taken to

go from 0 to 𝑎

2 is 𝑡1 and from

𝑎

2 to a is 𝑡2. Which relation for the

particle is correct?

Ans= (b) hint:- Y=𝑎 𝑠𝑖𝑛 𝜔𝑡

51. The output Y of the combination of gates for input A=0, B=0;

A=0, B=1 and A=1, B=1 respectively for the following circuit is

Ans= (c)

52. The dimension of Planck’s constant is equivalent to the

dimension of which of the following quantities?

Ans= (d)

53. A particle of mass m exhibiting simple harmonic motion has

potential energy V(𝑥)=a+𝑏𝑥2. The period of oscillation of the

particle is dependent on

Ans= (b)

54. A black hole is an object from which even light cannot

escape. A star of mass M, collapsing due to gravity, becomes a

black hole when its radius is R. At this stage, the density 𝜌 of the

black hole depends on M as

Ans= (d)

55. Two identical particles are projected horizontally in opposite

directions with a speed of 10𝑚𝑠−1 each from the top of a tall

building. Assuming g=10𝑚𝑠−2, the distance between them at the

MEE-2016 Physics


moment when their velocity vectors become mutually

perpendicular is

Ans= (c)

56. Which of the following plots is not a valid position-time

graph?

Ans= (b) hint:- at the same time a particle cannot be at diffract

places

57. A particle is confined to the region 𝑥≥0 by a one-

dimensional potential given by V (𝑥)=𝑢𝑜𝑥. Purely from

dimensional analysis point of view, the mean position of the

particle at temperature T is given by

Ans= (a)

58. A one-dimensional him rod of length L lies between 𝑥=0 and

𝑥=L as shown in the figure below

The mass/length of the rod is given by λ (𝑥) = 𝐾𝑥𝑀 , where K is a

constant. If the centre of mass of the rod at 𝑥 = 𝐿

3, then the value

of M is

Ans= (d)

59. Consider a system of two gas molecules with speeds 𝑣1 and

𝑣2. If the ratio of the r.m.s speed and the average speed of the

system is equal to 50

49, then

𝑣1

𝑣2 is equal to

Ans= (b)

60. Two point charges +𝑞1 and +𝑞2 are fixed with a finite

distance d between them. On the line joining the two charges, a

third charge 𝑞3 is placed in such a way that it remains in

equilibrium. This is

Ans= (c)

MEE-2016 Physics


61. A detective arrives at a murder scene around 8:00 p.m and

notes down the temperature of the corpse to be 29 ℃. After one

hour, he again notes down the same to be 25℃. If throughout

this duration, the temperature at the scene is held fixed at 21 ℃,

the murder took place at

Ans= (a) hint:- Newton’s cooling. 𝑇2−𝑇1

𝑡= 𝐾(

𝑇1+𝑇2

2− 𝑇𝑜)

62. The uncertainty over the mean value of the momentum 𝑝 of

a particle ∆𝑝. The uncertainty over the de Broglie wavelength, ∆𝜆

will be equal to

Ans= (b) hint:- ∆𝜆

𝜆=

∆𝑝

𝑝 ∆𝜆 =

𝜆∆𝑝

𝑝

63. Consider a sequential radioactive decay process A𝜆1→B

𝜆2→C,

with decay constants 𝜆1 and 𝜆2, such that 2𝜆1 = 𝜆2. At time t=0,

the number of sample A, 𝑁𝐴 (𝑡) is 𝑁0 and the numbers 𝑁𝐵(𝑡) and

𝑁𝐶(𝑡) of samples B and C respectively are zero. The maximum

value of 𝑁𝐵(𝑡) reached is

Ans= (b)

64. Consider three metal surfaces A, B and C with work

functions ф𝐴,ф𝐵 and ф𝐶 respectively. Given that ф𝐴 > ф𝐵 > ф𝐶.

The slopes of the graphs between the frequency of incident

radiation and maximum photoelectric energy for the three

surfaces, 𝑚𝐴, 𝑚𝐵 and 𝑚𝐶 are related by

Ans= (c) hint:- slope in same

65. Consider n charges distributed over a region of n concentric

spheres as shown in the figure below

In the 1irnit 𝑛 → ∞, the flux through the nth sphere is

approximately

Ans= (c)

MEE-2016 Physics


66. The Maxwellian distribution of molecular speeds at a

temperature T for a particular system of gas molecules is shown

below

If the temperature is raised to 2T, then the area under the curve

in the above plot

Ans= (c)

67. A particle moves under the influence of a force given by

𝐹 =

−𝐾 𝑥î + 𝑌ĵ +

2𝑧𝐾 .𝑊ℎ𝑖𝑐ℎ 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑠 𝑜𝑓 𝑚𝑜𝑡𝑖𝑜𝑛𝑠?

Ans= (d)

68. The moment of inertia of a straight wire about its

perpendicular bisector and that of a circular frame made of wire

about its perpendicular central axis are 𝐼1 and 𝐼2 respectively. If

the wires are of the same material and their lengths are identical,

the 𝐼1 / 𝐼2 is

Ans= (b) hint:- 2𝜋𝑅

69. Which of the following statements is incorrect?

Ans= (b)

70. An electron and a proton are accelerated through the same

potential difference. The ratio of their de Broglie wavelengths, 𝜆𝑒

/ 𝜆𝑝 is

Ans= (a) hint:- λ=ℎ

2𝑚𝑒𝑈

71. A point charge q of mass m is kept at a distance d below a

fixed charge –q as shown in the figure below

For what value of d, the charge q will remain stationary?

Ans= (a) hint:- coulomb force = weight of the change

MEE-2016 Physics


72. A solid sphere of radius R has a charge density given by 𝜌(r)

= K r, where K is a constant and r is the distance from the centre

of the sphere. The ratio of the magnitudes of electric field

intensities at r=𝑅

2 and r = R is

Ans=

73. The lowest value of potential energy for the hydrogen atom

electron is

Ans= (a)

74. The ratio of angular momentum of the hydrogen atom

electron in 𝑛=2 energy level and 𝑛=4 energy level is

Ans= (b)

75. The binding energy (in MeV) of a nucleus with mass number

A and charge Z is given by B=16A-16𝐴2/3 − 24(2𝑍−𝐴)2

𝐴−

3

4

𝑍2

𝐴1/3

The value of Z for the most stable isobar for A = 216 is

Ans= (d)

76. Consider the following two planetary systems

The orbits are circular and have the same radius. If 𝑀1 = 2𝑀2,

then the ratio of the orbital period of 𝑚1 to that of 𝑚2 is

Ans= (d) hint:- T=2⊼𝜋

∪

77. Which of the following graphs is the correct representation

of the plot between the wavelength of maximum radiation

(𝜆𝑚𝑎𝑥 ) and 𝛽 (=1

𝐾𝐵𝑇) of a blackbody?

Ans= (b)

78. Which of the following thermodynamic quantities is not an

extensive property?

Ans= (b)

MEE-2016 Physics


79. N capacitors with equal capacitances are first connected in

series and then in parallel. The ratio of the capacitance of the

first setup to the second in the limit N→ ∞ is

Ans= (a)

80. A simple pendulum of length 𝑙 is suspended from the ceiling

of an elevator accelerating upwards with a constant acceleration

a. Another identical pendulum is suspended from the ceiling of

an elevator accelerating downwards with a constant acceleration

a. For small oscillations, the ratio of the time periods of the two

pendulums (1st to the 2nd) is [a< 𝑔]

Ans= (a)

81. Two electrons move in circles of radii 𝑟1 and 𝑟2 under the

influence of a uniform magnetic field B. If 𝑟1

𝑟2=2, then the ratio of

the angular frequencies of the two electrons, 𝜔1

𝜔2 is

Ans= (d) hint:- r=𝑚∪

𝑞𝐵 𝑣 = 𝜔𝑟

82. The dimensions of 1

2𝜀

0𝐸2 (𝜀0 =permittvity of free space and

E= electric field) are

Ans= (c) hint:-Energy per unit volume =1/2(−0𝐸2

83. The motion of a body is given by the equation 𝑑𝑣(𝑡)

𝑑𝑡=6.0-3v(t)

where v (t) is the speed (in 𝑚𝑠−1) at time t (in seconds). The

speed of the body varies with time as

Ans= (b)

84. A ball is projected vertically upwards with a certain initial

speed. Another ball with twice the mass of the first ball is

projected at an angle of 60° with respect to the vertical with

MEE-2016 Physics


twice the initial speed of the first ball. At the highest point, the

ratio of their potential energies will be

Ans= (b) hint:- 𝐻1 =∪2

2𝑔, 𝐻2 =

∪2

8𝑔

85. An insect craw1s up inside a hemispherical surface very

slowly as shown in the figure below

The coefficient of friction between the insect and the surface is 1

2.

If the line joining the centre of the hemispherical surface to the

insect makes an angle α with the vertical, then the maximum

possible value of α is

Ans= (a) hint:- friction normal reaction

86. 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

Ans= (a)

87. A body of mass m moving with a velocity v in the 𝑥-direction

collides and sticks with another body of mass M moving with

velocity V in the Y-direction. The magnitude of the momentum of

the composite body is

Ans= (c)

88. A tube of length L is filled completely with an incompressible

liquid of mass M and closed at both ends. The tube is then

rotated in a horizontal plane about one of its ends with a uniform

angular velocity 𝜔. The force exerted by the liquid at the other

end is

Ans= (a)

89. Infinite number of masses, each of mass m, are placed along

a straight line at distances of r, 2r, 4r, 8r, etc., from a reference

point O. The gravitational field intensity at O will be

MEE-2016 Physics


Ans= (b)

90. The density of water at the surface of ocean is 𝜌. If the bulk

modulus of water is B, what is the density of ocean water at a

depth, where the pressure is 𝑛𝑜𝑃 , where 𝑃𝑜 is the atmospheric

pressure?

Ans=

91. A stone of relative density K is released from rest on the

surface of a lake. If viscous effects are ignored, the stone sinks in

water with an acceleration of

Ans= (c) hint:- 𝑔1 = 𝑔 (1 −1

𝑘)

92. A small metal sphere of radius r and density 𝜌 falls from rest

in a viscous liquid of density 𝜎 and coefficient of viscosity ŋ. Due

to friction, heat is produced. The rate of production of heat,

when the sphere has acquired the terminal velocity, is

proportional to

Ans= (c)

93. A spring of spring constant K is cut into two pieces such that

one piece is double the length of the other. The longer piece will

have a spring constant of

Ans= (b)

94. A uniform rope of mass M hangs vertically from a rigid

support. A block of mass m is attached to the free end of the

rope. A transverse pulse of wavelength λ is produced at the lower

end of the rope. The wavelength of the pulse when it reaches the

top of the rope is

Ans= (b)

MEE-2016 Physics


95. An ideal gas has pressure P, volume V and temperature T.

The ratio 𝐶𝑝 / 𝐶𝑉 = 𝑌 𝑎𝑛𝑑 𝑈 is the internal energy. If R is the gas

constant, then which of the following equations is not correct?

Ans= (a , d)

96. If a gas has 𝑓 degrees of freedom, then the ratio 𝐶𝑝 / 𝐶𝑉 of

the gas is

Ans= (d)

97. A spherical blackbody of radius 12cm radiates 450 W power

at 500 K. If the radius were halved and the temperature doubled,

then the power radiated would be

Ans= (d)

98. A layer of ice at 0℃ of thickness 𝑥1 is floating on a pond of

water. L, 𝜌 and K respectively are the latent heat of fusion of

water, density of ice and thermal conductivity of ice. If the

atmospheric temperature is –T ℃, then the time taken for the

thickness of layer of ice to increase from 𝑥1 to 𝑥2 is given by

Ans= (c)

99. Three charges Q, + q and + q are placed at the vertices of a

right – angled isosceles triangle as shown in the figure below

The net electrostatic energy of the configuration is zero if Q is

equal to

Ans= (b) hint:- use potential energy for a system of three

changes equation

100. If the potential difference between the plates of a capacitor

is increased by 20%, the energy stored in the capacitor increases

by exactly

Ans= (d)

the effective resistance between points p and q of the ... · the effective resistance between...

Documents