MH SET 2013: 17 February, Paper II, Physics
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Physics
Paper II
Time Allowed : 75 Minutes] [Maximum Marks : 100
Note : This paper contains Fifty (50) multiple choice questions, each question
carrying Two (2) marks. All questions are compulsory.
3. In an X-ray diffraction experiment
1. The trace of an antisymmetric
the incident radiation has a
matrix is : linewidth of 0.1%. Assuming ideal
situation what will be the angular
(A) real width δθ of a diffraction line at a
scattering angle of π/2 ?
(B) zero
(A) 0.001 rad
(C) pure imaginary (B) 0.01 rad
(C) 0.005 rad
(D) unity
(D) 0.002 rad
2. What is the volume of a
4. An experiment involves
parallelopiped spanned by the measurement of two random
variables A and B. The
vectors : measurement error in A is 0.1%
and that in B is 0.2%. The error
(iˆ + ˆj ) , ( ˆj + kˆ ) , (kˆ + iˆ) ? in measurement of (A + B) will
(A) zero then be :
(A) 0.1%
(B) 1
(B) 0.2%
(C) 2
(C) 0.03%
(D) 3
(D) 0.0225%
1 [P.T.O.
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5. The step function 6. The value of ∇(r2) is :
1 u>0
(A) r̂
θ (u) =
0 u<0
(B) 2 r
%
is given by the integral
(C) 2| r |
%
1 eizu
2πi ∫
C
z
dz
(D) zero
when the contour C is : 7. The value of ∇2(1/r) is :
(A) circle of radius a with origin as (A) −1 r 2
centre
(B) –4πδ(r)
(B) a semicircle comprising real
(C) 4π
axis and half the arc of circle
above the real axis (D) zero
(C) a semicircle as in (B) above but
8. If A is an antisymmetric matrix of
avoiding the origin by
odd order n, then the determinant
indenting the real axis by a
of A is :
semicircle of radius ε above the
real axis (A) positive real number
(D) a semicircle comprising the
(B) negative real number
imaginary axis and an infinite
arc of circle on the right side (C) zero
of origin (D) real number (–1)(n + 1)/2
2
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9. Band structure in crystalline 11. The maximal set of commuting
observables for a system in
structure is due to :
spherically symmetric potential is
(A) finite mass of electrons
given by :
(B) periodic nature of potential (A) H, L2, Lz
(C) uniform density of the solid (B) H, Lx, Ly, Lz
(C) p2, L2, Lz
(D) spherically symmetric nature of
(D) L2, Lz
the potential
12. Which of the following is not a
10. The ground state energy of a particle
consequence of Heisenberg’s
in infinite square well is 1 eV. If four
uncertainty principle ?
particles obeying Bose-Einstein
(A) Absence of electrons in atomic
statistics are kept in this well, then
nuclei
the ground state energy will be :
(B) Extra stability of benzene
(A) 30 eV molecule
(C) Repulsive part of van der
(B) 10 eV
Waals’ interaction
(C) 4 eV
(D) Antisymmetric nature of wave
(D) 1/4 eV function of electrons
3 [P.T.O.
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13. The stationary eigenfunction for 15. The wave function of a particle
Hamiltonian of a particle of mass m
moving in one-dimensional time
in one-dimensional potential V(x) is
given to be : independent potential V(x) is
ψ(x) = A exp(–bx2/2), represented by ψ(x) = e–iax + b, where
where A and b are real positive
a and b are real constants. This
constants. It follows that :
means that the potential V(x) is of
(A) V(x) = constant
the form :
(B) V(x) ∝ 1/x
(C) V(x) ∝ x2 (A) V(x) ∝ x
(D) V(x) ∝ x3
(B) V(x) ∝ x2
14. If the φ dependent part of an
(C) V(x) = constant
eigenfunction of an electron in a
hydrogen atom e 2iφ , then the
(D) V(x) = e–ax + b
minimum principal and minimum
orbital angular momentum 16. The eigenvalues of a Hermitian
quantum numbers n and l
operator must be :
respectively for this eigenfunction
will be : (A) Complex
(A) n = 3, l = 2
(B) Real
(B) n = 2, l = 2
(C) Positive
(C) n = 2, l = 1
(D) n = 1, l = 2 (D) Negative
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17. If the Q factor of a coil which is 19. It is required to operate a
W0L/R is measured as a function of
proportional counter with a
frequency, then :
maximum radial field of
(A) the plot between Q and
10 7 Vm –1 . The applied voltage
frequency is linear
required if the radii of the wire
(B) the value of Q initially
and tube are 0.002 cm and 1 cm
decreases with increase in
frequency and afterwards respectively is :
increases with increase in
(A) 107 Volts
frequency
(B) 1242 Volts
(C) the value of Q initially
increases with increase in (C) 1242 × 107 Volts
frequency and afterwards
decreases with increase in (D) 12 Volts
frequency 20. A pressure sensor measures the
(D) the Q factor remains constant systolic blood pressure of a human
irrespective of the value of
body which is 120 mm of Hg. It
frequency
means :
18. In a Millikan oil drop experiment,
one of the drop falls at speed V (A) Pressure is only 120 mm of Hg
without field and rises at speed 2 V
(B) Pressure is 120 mm of Hg above
with field E applied. If the field is
atmospheric pressure
made E/2, the drop will :
(A) fall with speed V/4 (C) Pressure is 120 mm of Hg below
(B) rise with speed V/2 atmospheric pressure
(C) rise with speed 3V/2 (D) It is noway related to
(D) remain steady atmospheric pressure
5 [P.T.O.
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21. In an individual thermistor, the 23. Formula for decibel is given as :
variation of resistance with
temperature is : decibels = 10 log
(A) Negative temperature coefficient If values of decibel is equal to zero
and non-linear then :
(A) Value of P2 is zero
(B) Negative temperature coefficient
(B) Value of P2 is greater than P1
and linear
(C) Value of P1 is ten times that
(C) Positive temperature coefficient of P2
and non-linear (D) Value of P1 is equal to value
of P2
(D) Positive temperature coefficient
24. If a signal is averaged ‘N’ times the
and linear signal to noise ratio improves by :
22. If a given signal consists of (A) N2 times
frequencies from 1 to 100 Hz. If (B) N times
the band limit frequencies for (C) N times
an amplifier are F 1 = 1 Hz,
F2 = 50 Hz N
(D) times
2
25. A cylindrical can filled with water
to a height of 40 cm has on its side
two small holes of equal area, one
at height of 10 cm and the other at
a height of 30 cm. At the initial time,
After amplification which of the what is the ratio of the mass of water
portion of the signal is affected flowing per second through the lower
more. hole to that flowing through the
upper hole ?
(A) P (A) 3
(B) T (B) 3
(C) R
(C) 5
(D) All (D) 5
6
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26. In the figure a frictionless, massless
pulley is fixed to the edge of a 28. Imagine the radius of the earth
frictionless table. The two blocks of
mass 10 kg and 5 kg are connected shrinking by 1%, its mass remaining
by a weightless string passing over
the pulley. Is the tension in the the same. Then its kinetic energy of
string :
(A) Greater than rotation :
(B) Less than
(C) Equal to (A) decreases by 2%
(D) Square of
the tension it would be if the 5 kg
(B) increases by 2%
block was glued down.
5 kg (C) increases by 1%
(D) decreases by 1%
29. A uniform thin rod of mass M and
10 kg
length L hangs from a frictionless
pivot and is connected at the bottom
27. A circular disc is rotating about its
centre in the horizontal plane. A by a spring to the wall as shown.
razor blade is balanced on edge in
a grove along a radius of the wheel. The spring constant is K. Then the
If the blade is pulled along the
radius toward the centre of the period of motion, is a function of :
wheel, will it tend to fall :
(A) In the direction of rotation
(A) M and K
(B) Opposite to the direction of
rotation
(C) On both sides with equal (B) K and L
probability
(D) In either in or opposite to the (C) M and L
direction of rotation depending
on the frictional force between
the edge and the disc (D) M, K and L
7 [P.T.O.
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32. The man in the figure weighs
30. What is the ratio of the mass of the 150 kg. He sits in a sling and pulls
himself slowly up by means of a rope
sun to the mass of the earth to one
one a pulley. With what force he
significant figure ? must pull ?
(A) 1 × 109
(B) 3 × 105
(C) 7 × 107
(D) 9 × 1011
31. Two persons of equal weights are
hanging by their hands from the (A) 150g
(B) 100g
ends of a rope hung over a (C) 75g
(D) 50g
frictionless pulley. They begin to g : constant acceleration due to
gravity on earth surface.
climb. One person can climb twice 33. A point charge q is placed at the
origin. The flux of the electric field
the speed of the other (with respect that passes through a square
described by the vertices (0, 0, 1),
to the rope). Who gets to the top (1, 0, 1), (1, 1, 1) and (0, 1, 1) is :
first ? q
(A) ∈
0
(A) faster climber q
(B) 3 ∈
0
(B) slower climber
q
(C) 6 ∈
(C) get there together 0
q
(D) indeterminate (D) 24 ∈
0
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34. In a constant electric field E , the 36. The Poynting vector
1
electric displacement vector D in S=
µ0
(E×B )
a certain dielectric medium is
has the dimension of :
found to be given by D = 2.1 ∈0 E .
(A) energy
This implies that the dielectric
(B) energy/area
medium is :
(C) power
(A) linear and isotropic (D) power/area
(B) linear and unisotropic 37. Which of the following equations
implies that magnetic monopole
(C) non-linear and isotropic
does not exist ?
(D) non-linear and unisotropic (A) ∇ × E = 0
(B) ∇ · B = 0
35. The electric potential in a region of
2 (C) ∇ × B = µ0 J
space is given by V = V0e–bx , where
∂ρ
V0 and b are constants. The volume (D) ∇ · J + =0
∂t
charge density in this region is : 38. The energy stored by an inductor is
(A) 0 in the form of :
(A) electric field
(B) 2b∈0xV
(B) magnetic field
(C) –2b∈0xV
(C) heat energy
(D) 2b∈0(1 – 2ax2)V (D) electrostatic potential energy
9 [P.T.O.
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39. A constant current is flowing 41. Considering Hydrogen (H 2) and
through a cylindrical wire. Then the
Helium (He) as classical ideal
Poynting vector at the surface of the
Maxwell-Boltzmann gas, the ratio of
cylindrical wire :
root mean square speeds of H 2
(A) is in the direction of the current
molecules to that of He atoms at the
(B) is in the radially outward
direction same temperature T is :
(C) is in the radially inward (A) 2
direction
(B) 2
(D) has zero magnitude
40. A charged particle q is kept at center 1
(C)
of a mettalic spherical shell. The 2
magnitudes of the electric fields
1
inside the shell and outside the shell (D)
2
are given by :
42. The molar specific heat of conduction
q
(A) 0, respectively electrons at 300 K is :
4 π ∈0 r 2
q 3
(B) , 0 respectively (A) >> R
2
4 π ∈0 r 2
3
q q (B) R
(C) 2 , respectively 2
4 π ∈0 r 4 π ∈0 r 2
3
q q (C) << R
(D) , respectively 2
4 π ∈0 r 4 π ∈0 r
(D) R
(r denotes the distance from the
center) Here R is the gas constant.
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43. Two identical particles are to 45. A system has a relaxation time of
be distributed over 3 energy
the order of a millisecond. A
levels. Treating the particles as
distinguishable Maxwell-Boltzmann quasistatic process on this system
particles, the number of ways in can be carried out on the time scale
which the particles can be
of the order of :
distributed is :
(A) 9 (A) 0.001 s
(B) 6 (B) 0.1 s
(C) 3
(C) 0.0001 s
(D) 8
(D) 1 µs
44. A system of N identical independent
three dimensional harmonic 46. Let E be the mean kinetic energy
oscillators vibrating with the same
and V be the volume of a classical
frequency ω. The system is contact
with a heat reservoir at temperature ideal gas. The pressure of the gas
T. Treating the oscillators as
is numerically equal to :
classical, the molar specific heat of
the system is : 2E
(A)
3V
3
(A) R 1E
2 (B)
3V
(B) 3NK
3E
(C)
3 2V
(C) R
2
1E
(D)
(D) 3R 2V
11 [P.T.O.
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47. In an adiabatic expansion of an
49. The equation of state of an ideal gas
ideal monatomic gas using Joule-
Thompson effect : in the extreme relativistic
(A) Cooling effect is produced
approximation is given by :
(B) Heating effect is produced
2
(A) PV = U
(C) Neither heating nor cooling 3
effect is produced 5
(B) PV = U
2
(D) Supercooling effect is produced
1
48. Which of the following thermo- (C) PV = U
3
dynamic relations is incorrect ?
2
(D) PV = U
∂F 5
(A) P = –
∂V T
50. The operator corresponding
∂G
(B) T = → → → →
∂T P to r · p − p· r in quantum
∂F
(C) S = – mechanics is :
∂T V
∂U (A) ih
(D) P = –
∂V S
Here P, V, T are the pressure, (B) zero
volume and temperature, and F, G,
S, U are the Helmholtz Free energy, (C) 3 ih
Gibbs’ free energy, entropy and
average energy respectively. (D) ( ∂ ∂ x + ∂ ∂ y + ∂ ∂ z)
12
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ROUGH WORK
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ROUGH WORK
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Source: Savitribai Phule Pune University. Question paper published by Savitribai Phule Pune University.