2 - RG Academy Ajmer

Transcription

[1]
AIPMT - 2015
Part - B
91.
A radiation of energy E falls normally on a perfectly
reflecting surface. The momentum transferred to the
surface is (C = Velocity of light)
(1)
E
c2
(2)
E
c
(3)
2E
c
(4)
2E
c2
Ans: [3] Momentum transferred to the surface 
a
Considering blocks B & C together,
b
94.
2E
(as it
c
A ship A is moving Westwards with a speed of
10 km h–1 and a ship B 100 km South of A, is moving
Northwards with a speed of 10 km h–1. The time after
which the distance between them becomes shortest is
(1) 10 2h
(4) 5 2 h
Ans: [3] The velocity of ship B w.r.t. A
95.
The
minimum
separation will
(4) 4 0 Aa 3
  q
E . dA  en
0
A, B and C are voltmeters of resistance R, 1.5 R and 3R
respectively as shown in the figure. When some
potential difference is applied between X and Y, the
voltmeter readings are VA, VB and VC respectively.
will
be perpendicular to
line joining A & B
and for that relative
distance
BP = 100 cos 45 0
100
km
2
Hence time at which it happens
d rel 100 / 2
5h
 tv 
10 2
rel
93.
(3) A 0a 2
bg
v BA  10 2 km / h N-E

(2) 4 0 Aa2
qen   0 A a  4a 2  4 0 Aa 3


BA
(1)  0 Aa 3
z
(3) 5 h


The electric field in a certain region is acting radially
outward and is given by E = Ar. A charge contained in
a sphere of radius a centred at the origin of the field,
will be given by
Ans: [4] Using Gauss's Law
(2) 0 h
occur when V
g
N  M B  MC a  6 N
is perfectly reflecting)
92.
F
 2 m / s2
M A  M B  MC
Three blocks A, B and C, of masses 4 kg, 2 kg and 1 kg,
respectively, are in contact on a frictionless surface, as
shown. If a force of 14 N is applied on the 4 kg block,
then the contact force between A and B is
(1) V A  VB  VC
(2) V A  VB  VC
(3) V A  VB  VC
(4) V A  VB  VC
Ans: [2] B and C are in parallel and their equivalent RBC  R
and hence V A  VB  VC
96.
In a double slit experiment, the two slits are 1 mm apart
and the screen is placed 1 m away. A monochromatic
light of wavelength 500 nm is used. What will be the
width of each slit for obtaining ten maxima of double
slit within the central maxima of single slit pattern?
(1) 0.02mm
(2) 0.2mm
(3) 0.1mm
(4) 0.5mm
Ans: [2] Here,
(1) 18 N
(2) 2 N
(3) 6 N
(4) 8 N
 a
2D 10D

a
d
2d
 0.2 mm
10
Ans: [3] Acceleration of blocks
"Guru-Kripa", Anasagar Circular Road, Ajmer 305 001 Tel: 0145-2631190, 2629236
[2]
97.
AIPMT - 2015
One mole of an ideal diatomic gas undergoes a
transition from A to B along a path AB as shown in the
figure
then as per Newton's law of gravitation force of
attraction between them is
F
GMm
, here G is gravitational constant
r2
The relation between G and K is described as
(1) K 
1
G
(2) GK  4 2
(3) GMK  4 2
The change in internal energy of the gas during the
transition is
(1) 12 kJ
(2) 20 kJ
(3) 20 kJ
(4) 20 kJ
Ans: [3] U  nCV T 

98.
b
(3)
Wd
x
2
3
and hence
4 2
K
GM
5
nRTB  nRTA
2
Then the output across RL will be
A rod weight W is supported by two parallel knife edges.
A and B is in equilibrium in a horizontal position. The
knives are at a distance d from each other. The centre of
mass of the rod is at distance x from A. The normal
reaction on A is
W dx
d
FG 4 IJ r
H GM K
100. If in a p-n junction, a square input signal of 10 V applied
as shown.
5
pBVB  p AV A  20 kJ
2
(1)
2
Ans: [3] T 
(4) K = G
g
(2)
Wx
d
(4)
W dx
x
b
g
Ans: [1] For equilibrium
(1)
(2)
(3)
(4)
Ans: [1] Diode will conduct only for forward bias.
101. Two particles of masses m1, m2 move with initial
velocities u1 and u2. On collision, one of the particles
get excited to higher level,after obsorbing energy  . If
final velocities of particles be v1 and v2 then we must
have
N A  NB  W
(1)
bg b g
F d  x IJW
G
H d K
and N A x  N B d  x
 NA
99.
Kepler's third law states that square of period of
revolution (T) of a planet around the sun, is proportional
to third power of average distance r between sun and
planet.
i.e. T2 = Kr3
here K is constant
1 2 2 1 2 2
1
1
m1 u1  m2 u2    m12 v12  m22v22
2
2
2
2
(2) m12 u1  m22 u2    m12 v1  m22 v2
(3)
1
1
1
1
m1 u12  m2 u22  m1 v12  m1 v22  
2
2
2
2
(4)
1
1
1
1
m1 u12  m2 u22    m1 v12  m2 v22
2
2
2
2
Ans: [4] Using energy conservation
1
1
1
1
m1u12  m2 u22    m1v12  m2 v22
2
2
2
2
If the masses of sun and planet are M and m respectively
[3]
AIPMT - 2015
102. Which of the following figures represent the variation
of particles momentum and the associated de-Broglie
wavelength?
Ans: [3] Here
so, a  v
(1)
dv
 2n 2 x 4 n 1
dx
106. The refracting angle of a prism is A, and refractive index
of the material of the prism is cot (A/2). The angle of
minimum deviation is
(2)
(3)
dv
 2nx 2 n 1
dx
(1) 1800 + 2A
(2) 1800 – 3A
(3) 1800 – 2A
(4) 900 – 2A
(4)
Ans: [3] n 
Ans: [3] p 
h
1
and hence p 


LM
N
A
2
sin A / 2
sin
min
sin
b g
so cot A / 2 
103. The approximate depth of an ocean is 2700 m. The
compressibility of water is 45.4 ×10–11 Pa–1 and density
of water is 103 kg/ m3. What fractional compression of
water will be obtained at the bottom of the ocean?
(1) 1.4 × 10–2
(2) 0.8 × 10–2
–2
–2
(3) 1.0 × 10
(4) 1.2 × 10
1
V / V
Ans: [4] Compressibility K   
B
P
V
 p K  gh K  12
.  102
 
V
b g b g
104. The two ends of a metal rod are maintained at
temperatures 1000C and 1100C. The rate of heat flow in
the rod is found to be 4.0 J/s. If the ends are maintained
at temperatures 2000C and 2100C, the rate of heat flow
will be
(1) 4.0 J/s
(2) 44.0 J/s
(3) 16.8 J/s
(4) 8.0 J/s
Ans: [1] H 
kAT
and since T is same, H remains same
L
105. A particle of unit mass undergoes one-dimensonal
motion such that its velocity varies according to
bg
v x  x
2 n
where  and n are constants and x is the position of
the particle. The acceleration of the particle as a function
of x, is given by
(1) 2n 2 e 4 n 1
(2) 2n 2 x 2 n1
(3) 2n 2 x 4 n1
(4)  2  2 x  2 n 1
LM
N
 cot A / 2  sin
or
OP
Q
A
2
A/2
min
LM
N
OP
Q
A
2
min
OP
Q
A  min  A 


2
2
2
or  min    2 A
107. A particle is executing SHM along a straight line. Its
velocities at distances x1 and x2 from the mean position
are V1 and V2 respectively. Its time period is
(1) 2
V12  V22
x12  x22
(2) 2
x12  x22
V12  V22
(3) 2
x22  x12
V12  V22
(4) 2
V12  V22
x12  x22
Ans: [3] Here, V1   A2  x12
and V2   A2  x22

v12
v22
2

x

 x22
1
2
2

1
x22  x12

 2 V12  V22
or T 2  4 2
or T  2
ex
j
2
2
 x12
V12
 V22
x22  x12
V12  V22
[4]
AIPMT - 2015
108. Two similar springs P and Q have spring constants KP
Ans: [4] Due to two semi infinite wires
LM OP ekj
N Q

i
Bwires  2 0
4R
and KQ, such that K P  KQ . They are stretched, first
by the same amount (case a), then by the same force
(case b). The work done by the springs WP and WQ are
related as, in case (a) and case (b), respectively.
(1) WP  WQ ; WQ  WP
(2) WP  WQ ; WP  WQ
(3) WP  WQ ; WP  WQ
(4) WP  WQ ; WQ  WP
1 2
kx or W  k
2
d
 WP  WQ K P  KQ
d i
111. A particle of mass m is driven by a machine that delivers
a constant power k watts. If the particles starts from
rest the force on the particle at time t is
Ans: [4] For case (A)
W
Due to semi-infintie loop

i
Bloop  0 i
4R
i
For Case (b)
(1)
1
mk t 1/ 2
2
(2)
mk 1/ 2
t
2
(3)
mk t 1/ 2
(4)
2mk t 1/ 2
2
1
F
W
or W 
K
2K
Ans: [2] At time t kinetic energy
1 2
mv  kt
2
Hence WP  WQ
109. Consider 3rd orbit of He+ (Helium), using non-relativistic
approach, the speed of electron in this orbit will be
[Given K = 9 × 109 constant, Z =2 and h (Planck's
Constant) = 6.6 × 10–34 J s]
8
(1) 3.0  10 m / s
6
(2) 2.92  10 m / s
(3) 1.46  106 m / s
(4) 0.73  106 m / s
Ans: [3] vn 
FG Z IJ FG c IJ
H n K H 137 K
 v3, He 
or
v
2 kt
m

a
dv

dt
so
F  ma 
k
2mt
mk 1/ 2
t
2
112. The fundamental frequency of a closed orgain pipe of
length 20 cm is equal to the second overtone of an
organ pipe open at both the ends. The length of organ
pipe open at both the ends is
2 3  108

 146
.  106 m / s
3
137
110. A wire carrying current I has the shape as shown in
adjoining figure. Linear parts of the wire are very long
and parallel to X-axis while semicircular portion of radius
R is lying in Y-Z plane. Magnetic field at point O is
(1) 140 cm
(2) 80 cm
(3) 100 cm
(4) 120 cm
v
3v
Ans: [4] 4  2
C
0
or  0  6 C  120 cm
113. An electron moving in a circular orbit of radius r makes
n rotations per second. The magnetic field produced at
the centre has magnitude.
(1)
 0ne
2r
(3) Zero
 0 I
i  2 k
(1) B 
4 R
e
 0 I
i  2 k
(2) B 
4 R
j
e
j


0 I 
 I 
i  2 k (4) B   0
i  2 k
(3) B  
4 R
4 R
e
j
e
Ans: [1] B 
j
(2)
 0ne
2r
(4)
 0n 2 e
r
b g
 0i  0 en

2r
2r
[5]
AIPMT - 2015
114. Two identical thin-plano-convex glass lenses (refractive
index 1.5) each having radius of curvatures of 20 cm are
placed with their convex surfaces in contact at the centre.
The intervening space is filled with oil of refractive index
1.7. The focal length of the combination is
(1) 50 cm
(2) – 20 cm
(1) 1 J
(2) 100 J
(3) –25 cm
(4) – 50 cm
(3) 99 J
(4) 90 J
Ans: [4] Here we have 3 thin lenses in contact.
g FGH 201  1 IJK  401 cm
b
1
1

 15
. 1
Now,
f1 f 3
w
h
b
i
g FGH
---1
l
IJ
K
1
TC
TC
9 QC
Ans: [4]  C  10  1  T  T  10  Q
H
H
H
For refrigerator, W  QC  QH
e
or 10  QC 
1
1
1
0.7
7
 1.7  1  

=
cm1
f2
20 20
10
100
so
1
as
10
heat engine, is used as refrigerator. If the work done on
the system is 10 J, the amount of energy absorbed from
the reservoir at lower temperature is
117. A carnot engine, having an efficiency of  
1
1
7
1
1



  cm1
f eq 40 100 40
50
----
f eq  50 cm
115. On observing light from three different starts P, Q and
R, it was found that intensity of violet colour is maximum
in the spectrum of P, the intensity of green colour is
maximum in the spectrum of R and the intensity of red
colour is maximum in the spectrum of Q. If TP, TQ and TR
are the respective absolute temperatures of P, Q and R,
then it can be concluded from the above observations
that
10
QC
9
QC  90 J

118. A mass m moves in a circle on a smooth horizontal
plane with velocity v0 at a radius R0. The mass is attached
to string which passes through a smooth hole in the
plane as shown.
The tension in the string is increased gradually and
(1) TP  TQ  TR
(2) TP  TQ  TR
finally m moves in a circle of radius
(3) TP  TR  TQ
(4) TP  TR  TQ
of the kinetic energy is
Ans: [3] Using wein's law
m 
1
T
since  v   G   R  TP  TR  TQ
116. If energy (E), velocity (V) and time (T) are chosen as the
fundamental quanties, the dimensional formula of
surface tension will be
2
1
(1) E V T
3
2
(2) EV T
1 2
(3) EV T
1
1 2
mv0
2
(2) mv02
(3)
1 2
mv0
4
(4) 2mv02
Ans: [4] Angular momentum of mass about centre remains
conserved. So
b
g
mv0 R0
L2
Kf 

2I f
mR02
2
4
F
GH
2
I  2 mv
JK
2
0
.
2 2
(4) EV T
Ans: [4] Let S  KE aV b T c (K is dimension less constant)
then ML0T 2 
(1)
R0
. The final value
2
LMeML T j e LT j bT g OP
N
Q
2
 a=1
2a + b = 0 or b = –2
and 2a  b  c  2
 c  2
2 2
So [S] = EV T
2 a
1 b
c
119. For a parallel, beam of monochromatic light of
wavelength  diffraction is produced by a single slit
whose widht a is of the order of the wavelength of the
light. If D is the distance of the screen from the slit, the
width of the central maxima will be
(1)
2Da

(2)
2D
a
(3)
D
a
(4)
Da

[6]
AIPMT - 2015
Ans: [2] The width of central maxima is
123. Figure below shows two paths that many be taken by a
gas to go from a state A to a state C.
2D
.
a
120. A wind with speed 40 m/s blows parallel to the roof of a
house. The area of the roof is 1250 m2. Assuming that
the pressure inside the house is atmospheric pressure,
the force exerted by the wind on the roof and the
direction of the force will be
(Pair = 1.2 kg/ m3)
(1) 2.4 ×105 N, downwards
In process AB, 400 J of heat is added to the system and
in process BC, 100 J of heat is added to the system. The
heat absorbed by the system in the process AC will be
(2) 4.8 ×105 N, downwards
(3) 4.8 ×105 N, upwards
(4) 2.4 ×105 N, upwards
Ans: [4] From Bernoulli's theorem
1
p  v 2  p0
2
Thus, F  pA 
1
p  v 2
2

FG n IJ
H 2K
F nI
(3) GH1  JK
3
FG 1 IJ
H nK
F 2I
(4) GH1  JK
n
(1) 1 
(2) 1 
(4) 460 J
Q AC  WAC  Q A B C  WA B C
or
degrees of freedom (n) is given by
(3) 500 J
U AC  U A B C
b g
CP
121. The ratio of the specific heats C   in terms of
V
(2) 380 J
Ans: [4] U AC  Q A B  C  WA B C
1 2
1
2
v A   12
.  40  250
2
2
 2.4  105 N upwards .
(1) 300 J
Q AC  Q A B C  WA B C  WAC  460J .
124. A block of mass 10 kg, moving in x direction with a
constant speed of 10 m s–1, is subjected to a retarding
force F = 0.1 x J/m during its travel from x = 20 m to 30 m.
Its final KE will be
(1) 250 J
(2) 475 J
(3) 450 J
(4) 275 J
z
30
Ans: [2] K f  Ki   Fdx
20
Ans: [4]
or K f 
27
13
122. If radius of the
the radius of
(1)
(3)
FG 13IJ
H 53K
125
53
b gb g
1
10 10
2
1/ 3
RAl
(2)
5
RAl
3
(4)
FG 53IJ
H 13K

g
01
. x dx  475 J
20
Al Nucleus is taken to be RAl, then
Te nucleus is nearly
zb
30
2
125. A conducting square frame of side a and a long striaght
wire carrying current I are located in the same plane as
shown in the figure. The frame moves to the right with
a constant velocity V. The emf induced in the frame will
be proportional to
1/ 3
RAl
3
RAl
5
Ans: [3] R  A1/ 3
FG IJ
H K
RTe
125

so
R Al
27
1/ 3

5

3
RTe 
5
R Al .
3
1
(1) 2 x  a 2 x  a
b
1
(3) 2 x  a
b
gb
g
2
g
(2)
1
x2
1
(4) 2 x  a
b
g
2
[7]
AIPMT - 2015
128. A block A of mass m1 rests on a horizontal table. A light
string connected to it passes over a frictionless pulley
at the edge of table and from its other end another black
B of mass m2 is suspended. The coefficient of kinetic
Ans: [1]
LM
MM
N
OP
PP
Q
 I
1
1
  B1  B2 va  0

va
2 x  a x  a
2
2
b


g
friction between the block and table is  k . When the
block A is sliding on the table, the tension in the string
is
b
g
b
2
1
b2 x  agb2 x  ag
.
k
1
2
1
k
k
1
(2)
2
2
126. Three identical spherical shells, each of mass m and
radius r are placed as shown in figure. Consider an axis
XX' which is touching to two shells and passing
through diameter of third shell.
bm   m g g
bm  m g
m m b1  g g
(4)
bm  m g
m1m2 1  k g
m1  m2
g
bm   m g g
(3)
bm  m g
bm   m gg ...(i)
Ans: [4] a 
(1)
1
1
2
2
k
1
2
1
m1  m2
Moment of inertia of the system consisting of these
three spherical shells about XX' axis is
T   k m1 g  m1a
for block m1,
(1) 4mr 2
(2)
11 2
mr
5
T  m1a   k m1 g ...(ii)
From equation (i) and (ii),
(3) 3mr 2
(4)
16 2
mr
5
T
Ans: [1] I 
LM
N
OP
Q
2 2
2
mr  2 mr 2  mr 2  4mr 2
3
3
127. Which logic gate is represented by the following
combination of logic gates?
(2) OR
(3) NAND
(4) AND
Ans: [4]
m1  m2
gg.
129. A certain metallic surface is illuminated with
monochromatic light of wavelength  . The stopping
potential for photo-electric current for this light is 3V0.
If the same surface is illuminated with light of
wavelength 2 , the stopping potential is V0. The
threshold wavelength for this surface for photo-electric
effect is
(1)
(1) NOR
b
m1m2 1   k

6
(2) 6
(3) 4 
Ans: [3]
(4)

4
b g
hc hc

 e 3V0 ...(i)
 0
hc hc

 eV0 ...(ii)
2  0
Solving above equations,  0  4 .
[8]
AIPMT - 2015
b g
130. When two displacement represented by y1  a sin t
b g
and y2  b cos t are superimposed the motion is
(1) simple harmonic with amplitude
ba  b g
133. A resistance R draws power P when connected to an
AC source. If an inductance is now placed in series
with the resistance, such that the impedance of the circuit
becomes 'Z' the power drawn will be
2
FG R IJ
H ZK
F RI
(4) PGH JK
Z
(1) P
(2) not a simple harmonic
a
2
LM
N
FG
H
2
2
1 b
Ans: [4] y  a  b sin t  tan a
 its an SHM with amplitude
R
Z
(3) P
a 2  b2
Ans: [2] Using
IJ OP
KQ
P i2R
131. A potentiometer wire has length 4 m and resistance
(2) 32 
(3) 40
(4) 44 
Ans: [2] Vpot =

FG Rpot IJ   FG1 mV  400 cmIJ
K
H Rpot + R K H cm
P
rms
2
for second case,
(1) 48
FG V IJ R
HRK
F V IJ R
P'  G
HZK
2
For first case,
a 2  b2 .
8  . The resistance that must be connected in series
with the wire and an accumulator of e.m.f. 2V, so as to
get a potential gradient 1 mV per cm on the wire is
2
(2) P
rms
FG R IJ .
H ZK
2

P' P
134. Across a metallic conductor of non -uniform cross
section a constant potential difference is applied. The
quantity which remains constant along the conductor
is
(1) Electric field
(2) current density
(3) current
(4) drift velocity
Ans: [3] Current remains constant.
R  32  .
132. Two spherical bodies of mass M and 5 M and radii R
and 2 R are released in free space with initial separation
between their centres equal to 12 R. If they attract each
other due to gravitation force only, then the distance
coverted by the smaller body before collision is
135. A parallel plate air capacitor of capacitance C is
connected to a cell of emf V and then disconnected
from it. A dielectric slab of dielectric constant K, which
can just fill the air gap of the capacitor, is now inserted
in it. Which of the following is incorrect?
(1) 1.5 R
(2) 2.5 R
(1) The charge on the capacitor is not conserved
(3) 4.5 R
(4) 7.5 R
(2) The potential difference between the plates
decreases K times
(3) The energy stored in the capacitor decreases K times
Ans: [4]
(4) The change in energy stored is
Total distance travelled by both to collide,
d = 9R = d1 + d2
Since no external force is involved,
or
IJ
K
Ans: [1] Since plates are isolated, charge on capacitor is
conserved.
X cm  0

FG
H
1
1
CV 2
1
2
K
b g b g
F 5 M IJ  9 R  7.5R .
d G
H 5 M  mK
M d1  5 M d 2
1

2 - RG Academy Ajmer

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