JEE MAIN - Physics (2003)

1
Which of the following atoms has the lowest ionization potential ?
Antwoord
(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
Antwoord
(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 $$k = 1.38 \times {10^{ - 23}}\,J/K$$ ]
Antwoord
(D)
$${10^9}\,\,K$$
4
In the middle of the depletion layer of a reverse- biased $$p$$-$$n$$ junction, the
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(B)
$$1.5$$ $$A$$
13
A $$220$$ volt, $$1000$$ watt bulb is connected across a $$110$$ $$volt$$ mains supply. The power consumed will be
Antwoord
(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
Antwoord
(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
Antwoord
(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 :
Antwoord
(A)
$$\sqrt 3 \,W$$
17
The magnetic lines of force inside a bar magnet
Antwoord
(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
Antwoord
(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
Antwoord
(D)
$$0.1$$ $$H$$
20
The core of any transformer is laminated so as to
Antwoord
(A)
reduce the energy loss due to eddy currents
21
To demonstrate the phenomenon of interference, we require two sources which emit radiation
Antwoord
(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
Antwoord
(B)
$${90^ \circ }$$
23
The image formed by an objective of a compound microscope is
Antwoord
(C)
real and enlarged
24
A strip of copper and another of germanium are cooled from room temperature to $$80K.$$ The resistance of
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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 :
Antwoord
(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
Antwoord
(D)
$${3 \over 2}$$
38
Which of the following parameters does not characterize the thermodynamic state of mattter?
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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 ?
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(D)
$$32 \times {10^{ - 32}}\,\,joule$$
52
Dimensions of $${1 \over {{\mu _0}{\varepsilon _0}}}$$, where symbols have their usual meaning, are
Antwoord
(C)
[ L²T^-2 ]
53
The physical quantities not having same dimensions are
Antwoord
(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
Antwoord
(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? $$\left[ {g = 10m/{s^2},\sin 30^\circ = {1 \over 2},\cos 30^\circ = {{\sqrt 3 } \over 2}} \right]$$
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(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
Antwoord
(D)
$$0.1$$ $$J$$