JEE MAIN - Physics (2003)

1
Which of the following atoms has the lowest ionization potential ?
Sagot
(B)
$${}_{55}^{133}\,Cs$$
2
The wavelengths involved in the spectrum of deuterium $$\left( {{}_1^2\,D} \right)$$ are slightly different from that of hydrogen spectrum, because
Sagot
(C)
the masses of the two nuclei are different
3
In the nuclear fusion reaction $$${}_1^2H + {}_1^3H \to {}_2^4He + n$$$
given that the repulsive potential energy between the two nuclei is $$ \sim 7.7 \times {10^{ - 14}}J$$, the temperature at which the gases must be heated to initiate the reaction is nearly
[ Boltzmann's Constant $$k = 1.38 \times {10^{ - 23}}\,J/K$$ ]
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(D)
$${10^9}\,\,K$$
4
In the middle of the depletion layer of a reverse- biased $$p$$-$$n$$ junction, the
Sagot
(A)
electric field is zero
5
Two identical photo-cathodes receive light of frequencies $${f_1}$$ and $${f_2}$$. If the velocities of the photo electrons (of mass $$m$$ ) coming out are respectively $${v_1}$$ and $${v_2},$$ then
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(A)
$$v_1^2 - v_2^2 = {{2h} \over m}\left( {{f_1} - {f_2}} \right)$$
6
If the binding energy of the electron in a hydrogen atom is $$13.6eV,$$ the energy required to remove the electron from the first excited state of $$L{i^{ + + }}$$ is
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(A)
$$30.6$$ $$eV$$
7
In an oscillating $$LC$$ circuit the maximum charge on the capacitor is $$Q$$. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is
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(C)
$${Q \over {\sqrt 2 }}$$
8
The length of a given cylindrical wire is increased by $$100\% $$. Due to the consequent decrease in diameter the change in the resistance of the wire will be
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(D)
$$300\% $$
9
The thermo $$e.m.f.$$ of a thermo -couple is $$25$$ $$\mu V/{}^ \circ C$$ at room temperature. A galvanometer of $$40$$ $$ohm$$ resistance, capable of detecting current as low as $${10^{ - 5}}\,A,$$ is connected with the thermo couple. The smallest temperature difference that can be detected by this system is
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(A)
$${16^0}C$$
10
An ammeter reads upto $$1$$ ampere. Its internal resistance is $$0.81$$ $$ohm$$. To increase the range to $$10$$ $$A$$ the value of the required shunt is
Sagot
(D)
$$0.09\,\Omega $$
11
The nagative $$Zn$$ pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by $$0.13g$$ in $$30$$ minutes. If the electrochemical equivalent of $$Zn$$ and $$Cu$$ are $$32.5$$ and $$31.5$$ respectively, the increase in the mass of the positive $$Cu$$ pole in this time is
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(C)
$$0.126$$ $$g$$
12
A $$3$$ volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The current $${\rm I}$$, in the circuit will be
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(B)
$$1.5$$ $$A$$
13
A $$220$$ volt, $$1000$$ watt bulb is connected across a $$110$$ $$volt$$ mains supply. The power consumed will be
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(C)
$$250$$ watt
14
A particle of mass $$M$$ and charge $$Q$$ moving with velocity $$\overrightarrow v $$ describe a circular path of radius $$R$$ when subjected to a uniform transverse magnetic field of induction $$B.$$ The network done by the field when the particle completes one full circle is
Sagot
(B)
zero
15
A particle of charge $$ - 16 \times {10^{ - 18}}$$ coulomb moving with velocity $$10m{s^{ - 1}}$$ along the $$x$$-axis enters a region where a magnetic field of induction $$B$$ is along the $$y$$-axis, and an electric field of magnitude $${10^4}V/m$$ is along the negative $$z$$-axis. If the charged particle continues moving along the $$x$$-axis, the magnitude of $$B$$ is
Sagot
(A)
$${10^3}Wb/{m^2}$$
16
A magnetic needle lying parallel to a magnetic field requires $$W$$ units of work to turn it through $${60^ \circ }.$$ The torque needed to maintain the needle in this position will be :
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(A)
$$\sqrt 3 \,W$$
17
The magnetic lines of force inside a bar magnet
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(D)
are from south-pole to north-pole of the Magnet
18
Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon
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(B)
relative position and orientation of the two coils
19
When the current changes from $$ + 2A$$ to $$-2A$$ in $$0.05$$ second, an $$e.m.f.$$ of $$8$$ $$V$$ is inducted in a coil. The coefficient of self- induction of the coil is
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(D)
$$0.1$$ $$H$$
20
The core of any transformer is laminated so as to
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(A)
reduce the energy loss due to eddy currents
21
To demonstrate the phenomenon of interference, we require two sources which emit radiation
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(D)
of the same frequency and having a definite phase relationship
22
To get three images of a single object, one should have two plane mirrors at an angle of
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(B)
$${90^ \circ }$$
23
The image formed by an objective of a compound microscope is
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(C)
real and enlarged
24
A strip of copper and another of germanium are cooled from room temperature to $$80K.$$ The resistance of
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(C)
copper strip decreases and that of germanium increases
25
The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the
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(B)
variation of the number of charge carries with temperature
26
Three charges $$ - {q_1}, + {q_2}$$ and $$ - {q_3}$$ are placed as shown in the figure. The $$x$$-component of the force on $$ - {q_1}$$ is proportional to
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(B)
$${{{q_2}} \over {{b^2}}} + {{{q_3}} \over {{a^2}}}\sin \theta $$
27
The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by
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(D)
Wien's law
28
A particle performing uniform circular motion has angular frequency is doubled & its kinetic energy halved, then the new angular momentum is
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(A)
$${L \over 4}$$
29
A circular disc $$X$$ of radius $$R$$ is made from an iron plate of thickness $$t,$$ and another disc $$Y$$ of radius $$4$$ $$R$$ is made from an iron plate of thickness $${t \over 4}.$$ Then the relation between the moment of inertia $${I_X}$$ and $${I_Y}$$ is
Sagot
(D)
$${I_Y} = 64{I_X}$$
30
Let $$\overrightarrow F $$ be the force acting on a particle having position vector $$\overrightarrow r ,$$ and $$\overrightarrow \tau $$ be the torque of this force about the origin. Then
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(D)
$$\overrightarrow {r.} \vec \tau = 0{\mkern 1mu} $$ and $$\overrightarrow {F.} \overrightarrow \tau = 0\,\,$$
31
The time period of satellite of earth is $$5$$ hours. If the separation between the earth and the satellite is increased to $$4$$ times the previous value, the new time period will become
Sagot
(C)
$$40$$ hours
32
The escape velocity for a body projected vertically upwards from the surface of earth is $$11$$ $$km/s.$$ If the body is projected at an angle of $${45^ \circ }$$ with the vertical, the escape velocity will be
Sagot
(C)
$$11$$ $$km/s$$
33
Two spherical bodies of mass $$M$$ and $$5M$$ & radii $$R$$ & $$2R$$ respectively are released in free space with initial separation between their centers equal to $$12R$$. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
Sagot
(C)
$$7.5$$ $$R$$
34
Three forces start acting simultaneously on a particle moving with velocity, $$\overrightarrow v \,\,.$$ These forces are represented in magnitude and direction by the three sides of a triangle $$ABC$$. The particle will now move with velocity
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(D)
$$\overrightarrow v \,\,,$$ remaining unchanged
35
A horizontal force of $$10$$ $$N$$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $$0.2$$. The weight of the block is
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(D)
$$2N$$
36
''Heat cannot by itself flow from a body at lower temperature to a body at higher temperature'' is a statement or consequence of :
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(A)
second law of thermodynamics
37
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $${C_p}/{C_V}$$ for the gas is
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(D)
$${3 \over 2}$$
38
Which of the following parameters does not characterize the thermodynamic state of mattter?
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(C)
Work
39
A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time $$'t'$$ is proportional to
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(B)
$${t^{3/2}}$$
40
A mass $$M$$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $$SHM$$ of time period $$T.$$ If the mass is increased by $$m.$$ the time period becomes $${{5T} \over 3}$$. Then the ratio of $${{m} \over M}$$ is
Sagot
(C)
$${16 \over 9}$$
41
Two particles $$A$$ and $$B$$ of equal masses are suspended from two massless springs of spring of spring constant $${k_1}$$ and $${k_2}$$, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $$A$$ and $$B$$ is
Sagot
(C)
$$\sqrt {{{{k_2}} \over {{k_1}}}} $$
42
The displacement of particle varies according to the relation
$$x=4$$$$\left( {\cos \,\pi t + \sin \,\pi t} \right).$$ The amplitude of the particle is
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(C)
$$4\sqrt 2 $$
43
The length of a simple pendulum executing simple harmonic motion is increased by $$21\% $$. The percentage increase in the time period of the pendulum of increased length is
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(D)
$$10\% $$
44
A body executes simple harmonic motion. The potential energy $$(P.E),$$ the kinetic energy $$(K.E)$$ and total energy $$(T.E)$$ are measured as a function of displacement $$x.$$ Which of the following statements is true ?
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(A)
$$K.E$$ is maximum when $$x=0$$
45
A metal wire of linear mass density of $$9.8$$ $$g/m$$ is stretched with a tension of $$10$$ $$kg$$-$$wt$$ between two rigid supports $$1$$ metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency $$n.$$ The frequency $$n$$ of the alternating source is
Sagot
(A)
$$50$$ $$Hz$$
46
The displacement $$y$$ of a wave travelling in the $$x$$-direction is given by $$$y = {10^{ - 4}}\,\sin \left( {600t - 2x + {\pi \over 3}} \right)\,\,metres$$$
where $$x$$ is expressed in metres and $$t$$ in seconds. The speed of the wave - motion, in $$m{s^{ - 1}}$$, is
Sagot
(A)
$$300$$
47
A tuning fork of known frequency $$256$$ $$Hz$$ makes $$5$$ beats per second with the vibrating string of a piano. The beat frequency decreases to $$2$$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
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(C)
$$256 - 5Hz$$
48
If the electric flux entering and leaving an enclosed surface respectively is $${\phi _1}$$ and $${\phi _2},$$ the electric charge inside the surface will be
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(A)
$$\left( {{\phi _2} - {\phi _1}} \right){\varepsilon _0}$$
49
A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor
Sagot
(B)
remains unchanged
50
A thin spherical conducting shell of radius $$R$$ has a charge $$q.$$ Another charge $$Q$$ is placed at the center of the shell. The electrostatic potential at a point $$P$$ a distance $${R \over 2}$$ from the center of the shell is
Sagot
(C)
$${{2Q} \over {4\pi {\varepsilon _0}R}} + {q \over {4\pi {\varepsilon _0}R}}$$
51
The work done in placing a charge of $$8 \times {10^{ - 18}}$$ coulomb on a condenser of capacity $$100$$ micro-farad is
Sagot
(D)
$$32 \times {10^{ - 32}}\,\,joule$$
52
Dimensions of $${1 \over {{\mu _0}{\varepsilon _0}}}$$, where symbols have their usual meaning, are
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(C)
[ L²T^-2 ]
53
The physical quantities not having same dimensions are
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(B)
momentum and Planck's constant
54
A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the same car is moving at a speed of 100 km/hr, the minimum stopping distance is
Sagot
(C)
24 m
55
A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of $$30^\circ $$ with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground? $$\left[ {g = 10m/{s^2},\sin 30^\circ = {1 \over 2},\cos 30^\circ = {{\sqrt 3 } \over 2}} \right]$$
Sagot
(D)
8.66 m
56
The co-ordinates of a moving particle at any time 't' are given by x = $$\alpha $$t³ and y = βt³. The speed to the particle at time 't' is given by
Sagot
(B)
$$3{t^2}\sqrt {{\alpha ^2} + {\beta ^2}} $$
57
A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads $$49$$ $$N,$$ when the lift is stationary. If the lift moves downward with an acceleration of $$5 m/{s^2}$$, the reading of the spring balance will be
Sagot
(A)
$$24$$ $$N$$
58
A light spring balance hangs from the hook of the other light spring balance and a block of mass $$M$$ $$kg$$ hangs from the former one. Then the true statement about the scale reading is
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(A)
Both the scales read $$M$$ $$kg$$ each
59
A marble block of mass $$2$$ $$kg$$ lying on ice when given a velocity of $$6$$ $$m/s$$ is stopped by friction in $$10$$ $$s.$$ Then the coefficient of friction is
Sagot
(D)
$$0.06$$
60
A block of mass $$M$$ is pulled along a horizontal frictionless surface by a rope of mass $$m.$$ If a force $$P$$ is applied at the free end of the rope, the force exerted by the rope on the block is
Sagot
(D)
$${{PM} \over {M + m}}$$
61
A rocket with a lift-off mass $$3.5 \times {10^4}\,\,kg$$ is blasted upwards with an initial acceleration of $$10m/{s^2}.$$ Then the initial thrust of the blast is
Sagot
(A)
$$3.5 \times {10^5}N$$
62
Consider the following two statements :

$$A.$$ Linear momentum of a system of particles is zero

$$B.$$ Kinetic energy of a system of particles is zero.

then
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(A)
$$A$$ does not imply $$B$$ and $$B$$ does not imply $$A$$
63
A spring of spring constant $$5 \times {10^3}\,N/m$$ is stretched initially by $$5$$ $$cm$$ from the unstretched position. Then the work required to stretch it further by another $$5$$ $$cm$$ is
Sagot
(B)
$$18.75$$ $$N$$-$$m$$
64
A wire suspended vertically from one of its ends is stretched by attaching a weight of $$200N$$ to the lower end. The weight stretches the wire by $$1$$ $$mm.$$ Then the elastic energy stored in the wire is
Sagot
(D)
$$0.1$$ $$J$$