2. Hcu Msc 2018.pdf

fiziks Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    HCU (M. Sc) 2018 Q1.

If z  x  iy the function of f  z  

(a)

(c) Q2.

1 x

1  x 

2

y

2

1 y

1  y 

2

x

2

i i

1 can be expressed in the form u ,  x, y   iv  x, y  as 1  z*





y

1  x 

2

y

2

x

2

x

1  y 

2

(b)

(d)

1 x

1  x 

2

y

2

1 y

1  y 

2

x

2

i i

y

1  x 

2

 y2

x

1  y 

2

 x2

The matrix 0 0 1 M   0 1 0  is 1 0 0   (a) Hermitian but not unitary

Q3.

Q4.

(b) Unitary but not hermitian

(c) Unitary as well as hermitian (d) Neither hermitian nor unitary   If curl of a vector field F vanishes then F can always be written as (a) gradient of a scalar potential

(b) curl of a vector potential

(c) divergence of a vector potential

(d) constant times a scalar potential

The tensile strength of a wire is given by (a) the ratio of the maximum load to which the wire is subjected to the original cross-sectional area of the wire. (b) the ratio of the minimum load to which the wire is subjected to the original cross-sectional area of the wire. (c) the strength of the wire up to which it obeys Hooke’s law. (d) the ratio of the residual strain in the wire to the original cross-sectional area of the wire.

Q5.

For a liquid with density  , flowing horizontally, the pressure and velocity at one point P1 and

v1 and at another point P2 and v2 respectively, are related by the following equation v12 P2 v22 (a)     2  2 P1

(c)

P1





v12 P2 v22   2  2

v12 P2 v22 (b)     2  2 P1

(d)

P1





 P v2  v12  1 2  2  2  2

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1 

fiziks Q6.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    Consider a spherical soap bubble and spherical water drop which are identical in volume and

have same surface tension. If Pb and Pd represent the excess pressure inside the soap bubble and P  water drop respectively, then the ratio  b  is equal to  Pd 

(a) 4 Q7.

(b) 2

(c) 1

(d) 0.5

A simple harmonic oscillator has velocities v1 and v2 at positions x1 and x2 (from the equilibrium point) respectively. The frequency of the oscillator is given by

v (a) x Q8.

 x 

2 1

 v22

2 1

2 2

v (b) x

 x 

2 1

 v22

2 1

2 2

(c)

v x

 x 

2 1

 v22

2 2

2 1

(d)

v x

 x 

2 1

 v22

2 1

2 2

If a point object moves in a plane according to x  a sin t and y  a sin 2t , the trajectory equation of the object is given by (a) y  x  



2x x2  a2



a2

(b) y  x   x 1 

x2 a2

x2 x2 (d) y x  2 x 1    a2 a2 A cylinder with insulating wall contains N atoms of a perfect gas. The cylinder is permanently

(c) y  x   1  Q9.

closed at one end and the other end is closed with a piston. The initial volume is V1 and the initial temperature is T1 . If the volume is suddenly increased to V2 by shifting the piston outward, then the change in internal energy is given by

Q10.

(a) dU  P V2  V1 

(b) dU  0

(c) dU  R T2  T1 

(d) dU  P V2  V1  / T

When a gram-atomic Wight of silver is heated at constant volume from 0o C to 30o C , CV  5.85 Cal/deg.mole, then change in entropy is (a) 0.92 Cal/K

Q11.

(b) 0.54 Cal/K

(c) 0.61 Cal/K

(d) 0.32 Cal/K

A microscope is focused on an object. A parallel sides glass plate of refractive index n and thickness d is inserted between the object and the microscope objective, and the microscope is now refocused. If x is the distance the microscope is moved in refocusing, then x is equal to (a) 1  n  d

(b)  n  1 d

1   (c) 1    nd 

 1 (d) 1   d  n

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2 

fiziks Q12.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    A metal can be modelled by a system of free electrons of mass m and charge e . Assume that

the resistively of such a system arises only from the collision between electrons. If the electron density is n and mean free time between two collision is  , then according to Drude’s theory the conductivity of the metal can be written as ne2T n 2 eT neT 2 ne2T (b) (c) (d) m2 m m m The potential at a distance r from an electric dipole is proportional to 1 1 1 1 (b) 2 (c) r 0 (d)  2 (a) r r r r The electric field at a point P  x, y, z  in space is given by  A ˆ E  x, y , z   i 6 x  ˆj 2 y  kˆ3 z 0 L3 (a)

Q13.

Q14.





Where L is a length and K is constant. The charge density at the point P  x, y, z  is given by (a) Q15.

Q16.

7A L3

(b)

11A L3

(c)

2A L3

(d)

A L3

Which of the following does not obey the super-position principle? (a) Electrostatic force

(b) Electric field

(c) Electrostatic potential

(d)Electrostatic energy

A charged particle moves in a plane perpendicular to a magnetic field B . If it starts with some additional speed v parallel to B , the trajectory of the charged particle will be (a) circular

Q17.

(b) elliptical

(c) parabolic

(d) helical

Consider the following steady current configuration where I is the current and r1 , r2 are the radii of the two concentric semicircles. The magnetic field at the point P is given by I 0 I  1 1  0 I  1 1  (a) B  (b) B        r2 4  r1 r2  8  r1 r2  (c) B 

Q18.

0 I  1

1    2  r1 r2 

(d) B  0

r1 P

It is given that the average power dissipated by an A.C circuit is zero. The circuit contains (a) only pure resistive elements

(b) only pure reactive elements

(c) both resistive and reactive elements

(d) nonlinear elements.

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3 

fiziks Q19.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    Which of the following wave does represent the Out-put voltage that is drawn across the

practical silicon diode in the circuit? R

Vm   5 V

Vout

5V (a)

(c)

0

0

4.3V

 2



2

3

3

4

(b)

5

4

(d) 7V 0

2 3

4

5

4

Which of the following is a valid Boolean expression? (a) A  AB  A  B

Q21.



3

5V

5V Q20.

 2

0

(b) A  AB  A

(c) A  AB  A

(d) A  AB  B

Which of the following statements is true for the partical silicon connected in the circuit shown 10 k 

in the figure below?

5V

D2

D1

D3

(a) D1 is forward biased, D 2 and D3 are reverse biased (b) D 2 and D3 are forward biased, D1 is reverse biased (c) D1 is forward biased and either D 2 or D3 is forward biased (d) All three diodes ( D1, D 2 and D3 ) are forward biased

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4 

fiziks Q22.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    The length of a spaceship is measured to be half its actual length by an observer. What is the

speed of spaceship relative to the observer?

Q23.

(a) 2.598 108 m / s

(b) 3.543 108 m / s

(c) 5.234  108 m / s

(d) 7.823 108 m / s

Aˆ , Bˆ and Cˆ are Hermitian operators, where Aˆ and Bˆ do not have simultaneous eigen functions. Which of the following relation can be true?





(a) Aˆ , Bˆ   Cˆ

Q24.



(b) Aˆ , Bˆ  Cˆ



(c) Aˆ , Bˆ   0



(d) Aˆ , Bˆ   iCˆ

Consider a particle confined in a one-dimensional box of length L . The energy spacing between any two consecutive energy levels is proportional to

Q25.

(b) L (c) L1 (d) L2 (a) L2 The specific heat of an ideal classical gas of N molecules at temperature T is equal to 1 3 (a) Nk BT (b) Nk BT (c) Nk B T (d) 3Nk B T 2 2

Q26.

SECTION - B    Given the three vectors A  3iˆ  2 ˆj  kˆ, B  6iˆ  4 ˆj  2kˆ and C  iˆ  2 ˆj  kˆ , which of the

Q27.

following relations is true?     (a) A || B and B  C (b)     (c) B || C and A  B (d) 1 and 2 are two eigenvalues of the matrix

    A || C and B  C     A || B and B || C

p r M  .  s p

Then the value of  1  2  will be 2

(a) p 2  rs

Q28.

(b) 4 p 2  rs

(c) 4rs



(d) 4 p 2  rs



The sum 

1

  2n  1 2n  1 n 1

is equal to (a) 1

(b)

1 2

(c)

1 4

(d)

1 8

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5 

fiziks Q29.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    If n is greater than 1 , then

1  n   ln   n  n 1  is

Q30.

(a) greater than 1

(b) greater than 0 but less than 1

(c) less than 1

(d) equal to 1

The sum of the series 1 1 1 1 1 1       .... 3 5 7 9 11 is equal to (a)

Q31.



(b)

2



(c) 

4

Which of the following can be the square of i

Q32.

1 2

1  i  ,

1 2

100 101



1 ?

1 1 1  i  ,  1  i  2 2 1 (d) 1  i  , 1  i  2

(a) 1  i  ,  1  i  (c)



(d)

(b)

1  i 

What is the angular momentum of the electron in a hydrogen atom about its nucleus? It is given that the mass of electron is 9.111031 kg and the radius of electron orbit is 0.58  1010 m

Q33.

(a) 2.28 1034 kgm 2 s 1

(b) 1.06  1034 kgm 2 s 1

(c) 4.43  1032 kgm 2 s 1

(d) 6.28  1032 kgm 2 s 1

Two blocks of masses m1  1.3 kg and m2  2.8 kg are connected by a cord of negligible mass over a frictionless pulley. The magnitude of the block acceleration and the tension in the cord are given by

Q34.

(a) 5.2 m / s 2 and 16 N

(b) 3.6 m / s 2 and 17 N

(c) 5.2 m / s 2 and 10 N

(d) 5.2 m / s 2 and 12 N

Two gravitationally bound stars with equal masses m , separated by a distance d , revolve about their centre of mass in circular orbits. The period of their motion is proportional to 1/ 2

 d3  (a)   m

1/ 2

 d3  (b)  2  m 

1/ 3

 d2  (c)  3/ 2  m 

d (d)   m

3/ 2

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6 

fiziks Q35.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    Consider a particle of mass m whose motion starts from rest in a constant gravitational field. If a

resisting force equal to kmv 2 where v is the velocity of the particle and k is a constant, is encountered by the particle, then what is the distance the particle falls in accelerating from velocity v0 to v1 ?  g  kv02  (a) k ln  2  g  kv1 

(c) Q36.

1  g  kv02  (b) ln   k  g  kv12 

1  g  kv02  ln   2k  g  kv12 

(d)

2  g  kv02  ln   k  g  kv12 

The speed of a particle of mass m varies with the distance x as v  x   ax  n . Assume v  x  0   0 at t  0 . The force F  t  responsible s proportional to

(a) t  2 n 1 /  n 1 Q37.

(b) t  n 1 /  2 n 1

(c) t  2 n 1 /  n  2

(d) t  n  2 /  2 n 1

Consider a particle of mass m suspended between two identical springs. The mass m is displaced towards right by distance x (much smaller than l ) as shown in figure and then left to oscillate. In leading order, the acceleration of the mass is proportional to

s

t x

m



t

(a) Equilibrium position (a)  x Q38.

(b)  x 2

m

s

(b) Extended position (c)  x3

(d) e x

The motion of the cyclonic wind is (a) anticlock wise in both northern and southern hemispheres (b) clock-wise in both northern and southern hemispheres (c) clock-wise in northern hemisphere and anticlock-wise in southern hemisphere. (d) anticlock-wise in northern hemisphere and clock-wise in southern hemisphere.

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7 

fiziks Q39.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    What is the dimension of viscosity   ?

(a) M 1 L1T 1 Q40.

(b) M 1 L1T

(c) ML1T 1

(d) MLT 1

A rod is subjected to uniaxial load within linear elastic limit. When the change in the stress in 300 Mps, the change in the strain is 0.001 . If the Poisson ratio of the rod is 0.5 , the modulus of

rigidity in  GPa  is (a) 0.1GPa Q41.

(c) 10.0GPa

(d) 100.0GPa

Strain due to two equal tensile stresses will be zero only if the value of Poisson ratio is (a) less than 1

Q42.

(b) 1.0GPa

(b) greater than 1

(c) equal to 1

(d)equal to 1

In an acoustic resonance experiment, if the distance between the adjacent positions of the piston at which resonance is observed at a frequency 2000 Hz is equal to 8.5 cm , the velocity of sound is (a) 3.4 km / s

Q43.

(b) 0.34 km / s

(c) 34.0 cm / s

(d) 0.34 cm / s

Consider a sonometer wire made by soldering two wires of radii r and 2r and kept under tension T . Stationary vibrations are setup in the wire such that the soldered joint is midway between the two bridges and is a node. The ratio of the number of loops formed in the wires is (a) 1

Q44.

(b) 2

(c)

1 2

(d)

1 4

Consider that a source of sound vibrations with frequency 1700 Hz and a receiver are located on the same normal to the wall. With both the source and the receiver stationary, the wall recedes from the source with velocity 6.0 m / s . If the velocity of sound is 340 m / s , the best frequency measured by the receiver will be (a) 0.6 Hz

Q45.

(b) 6.0 Hz

(c)

1 Hz 6

(d) 1.6 Hz

An electromagnetic wave of frequency 3 MHz passes from vacuum into a dielectric medium with permittivity  4.0 . The change in wave length is (a) 100 m

(b) 0 m

(c) 50 m

(d) 50 m

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8 

fiziks Q46.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    A simple harmonic oscillator of mass m and frequency 0 is initially described by the equation:

 x  02 x  0 . A forcing force mf 0it is now applied to drive the oscillator. The particular solution for x can in general be written as (a) Q47.



f 0 eit

2 0

 2



(b)



f 0 eit 2 0

 i 2



(c)

f 0 eit

0  i 

2

(d)



f 0 eit 2 0

 2



The electron in an excited atom behaves like a damped harmonic oscillator when the atom radiates light. The lifetime of an excited atomic state is 108 s and the wavelength of the emitted light is 500 nm . The qulity factor is given by (a) 4 107

Q48.

(b) 4 109

(c) 4 105

(d) 4 103

Consider that idealized Sun and Earth both are black bodies. The Sun’s surface temperature Ts is 6000 K . The radius of the earth is 6 108 cm and the radius of the Sun is 7 1010 cm . Distance to Sun from earth is 1AU  1.5 1013 cm . Assume that heat transfer by ocean and atmosphere on earth is so efficient as to keep earth’s surface at uniform temperature. What is the temperature of earth? (a) 12o C

Q49.

(b) 17o C

(c) 20o C

(d) 15o C

A pin-hole camera forms an image of a distant object on a screen at a distance d from the pinhole. If R is the pin-hole radius and  is the wavelength of light the value of R that gives the sharpest image is (a)

Q50.

0.61 d

(b) 0.61 d

(c)  d / 0.61

(d) 0.61/  d

A plane wave of 500 nm wavelength is incident normally on a mask containing a 1 mm diameter hole. The farthest distance from the mask at which one can observe a diffraction pattern with zero intensity at the center is (a) 25 mm

(b) 500 mm

(c) 250 mm

(d) 50 mm

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9 

fiziks Q51.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    A lens corrected for spherical aberration is used to image a distant axiant point source of

wavelength  . The lens has diameter d and length f . How close to thee focal point, on the axis, will it be possible to detect that the image is out of focus?  f2 (a) 2  2  d 

Q52.

 f  (b) 2   d

(c)



(d)

2



  d2    2 f2



Consider a right-angle triangle prism 450  450  900 made of MgF2 of refractive idex 1.38 . A right circular polarized light beam incident on the hypotenuse and reflected by 900 via total internal reflection (as shown) becomes (a) linearly polarized parallel to the plane of incidence (b) right circularly polarized (c) left circularly polarized

Q53.

(d) linearly polarized perpendicular to the plane of incidence  A electric dipole p is kept at the origin of the upper hemisphere of radius R as shown in the z figure  P

y

R

x The electric flux through the surface of the upper hemisphere is given by (a) Q54.

p 2 0 R

(b)

p 0 R

(c)

p 4 0 R

(d)

3p 4 0 R

Consider a capacitor consisting of two coaxial cylinders of height h and radii r1 and r2 . The capacitance of this capacitor is proportional to r  (a) h ln  2   r1 

1 r  (b) ln  2  h  r1 

(c)

h r  ln  1   r2 

(d)

h r  ln  2   r1 

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fiziks Q55.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    Consider a parallel plate capacitor with circular plates each of radius r . The separation between

the plates is d  r  d  . The capacitor is charged to a potential V and then disconnected from the charging circuit. The separation of the plates is now slowly changed from d to d  . The work done in this process is proportional to (a)

(c) Q56.

r 2  d   d V 2

(b)

d2 r  d   d V 2

(d)

d

r  d   d V 2 d2 r 2 dV 2

d  d 

2

Consider a uniformly charged circular ring of radius a . The electric field at a point on the axis of the ring at a distance x fro the centre of the ring is proportional to (a)

Q57.

x

a

2

 x2 

3/ 2

(b)

x4

a

2

 x2 

3

(c)

x2

a

2

 x2 

2

(d)

1

a

3

 x3 

2/3

An air spaced coaxial cable has an inner conductor 0.5 cm in diameter and an outer conductor 1.5 cm in diameter. The inner conductor is at a potential 8000V with respect to the grounded outer conductor. What is the electric field at r  1 cm? (a) 8000V / m

Q58.

(b) 4000 V / cm

(c) 0 V / m

(d) 5333.333V / m

In the following circuit each resistor is of resistance 1 ohm. What is the net resistance between

A and B if the chain is infinite length? A

B

(a) Q59.

5/3

(b)





5 1 / 3

(c)





5 1 / 2

(d)





5 2 /2

Consider an infinitely long and straight conductor carrying a current I . What is the magnetic field produced by this current at a point which is a distance R from the conductor? (a)

4I cR

(b)

2I cR

(c)

cI 2R

(d)

2I c2 R

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fiziks Q60.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    A uniform magnetic field B has been applied in the z direction. Which of the following vector

can describe the vector potential?

Q61.

 1  (a)   yB, xB, 0   2 

(b)   yB, xB, 0 

1  1  (c)   xB, yB, 0  2  2 

(d)  0, xB, 0 

Which of the following is the correct boundary condition in magnetostatics at a boundary between two different media? (a) The tangential component of B is continuous (b) The normal component of B is continuous (c) The normal component of H is continuous (d) None of the above

Q62.

A very long straight solenoid of n turns per unit length carries a current i which increases uniformly with time i  kt where k is a constant. What is the magnitude of the magnetic field inside the solenoid at time t ? (a) 0 nkt

Q63.

(b) 0 n 2 kt

(c) 0 nkt 2

(d) 0  ln n  kt

A particle with charge q is travelling with velocity v parallel to a wire with a uniform charge distribution  per unit length. The wire

z

also carries a current I shown in figure below. What must the velocity be for the particle to travel in a straight line parallel to the

I

wire, a distance r away?



(a)

(c)

 cI qv

c2 qI

(b)

(d)

c2 I

0

v r q

c2 vI

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fiziks Q64.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    Which of the following is a correct and simplest expression for the Boolean function Y 

described by the Karnaugh map?

BC 1

A

1

BC 1

X

X

 (c) Y  C  AB

 (b) Y  C

(a) Y  C

  (d) Y  BC  AC

Which of the following pair of equations is correct for the circuit shown in figure? XC 2 R=6

5 V L 00

X L 5 

I1

I2

10 V L 00

Q65.

A

BC

BC

(a) 11I1  6 I 2  5;6 I1  8 I 2  10 (b)  6  5 j  I1  6 I 2  5;6 I1   6  2 j  I 2  10 (c)  6  5 j  I1  6 I 2  5;6 I1   6  2 j  I 2  10 (d) I1  6 I 2  5;6 I1  4 I 2  10 Q66.

The voltage VAB  across the terminals A and B in the circuit is equal to A

B

1.7 k 1.7 k

12V

3 k 6 k

1.7 k

3 k

15V

1.7 k

(a) 3.5V

(b)1.5 V

(c) 3 V

(d) 3.5V

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fiziks Q67.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    In a common emitter transistor circuit, the collector resistance  Rc  is 4 k , emitter resistance

 RE 

is zero,  of the transistor is 100 and the biasing voltage VCC  is 10V . What is the

collector current  I C  . If the base current  I B  is 50  A (a) 5 mA Q68.

(b) 20 mA

(d) 2 mA

Te relativistic momentum of a neutron (rest mass energy m0 c 2  940 MeV ), whose kinetic energy

 K   200 MeV

Q69.

(c) 100 mA

is given by

(a) 1050 MeV / C

(b) 750 MeV / C

(c) 645 MeV / C

(d) 350 MeV / C 0

The diameter of Bohr’s first orbit is 1.058 A . The de Broglie wavelength of electrons in this orbit is 0

(a) 0.53 A Q70.

0

(b) 1.058 A

0

0

(c) 0.4 A

(d) 3.33 A

Te distance of closest approach of a 5.30 MeV  -particle to a Cu  Z  29  nucleus in a head on collision is (a) 1.57 1014 m

(b) 1.02 1014 m

(c) 2.3 1014 m

(d) 5.11014 m 0

Q71.

A  - ray beam from Cs137 sample with wavelength 0.0188 A is scattered by a free electron. If the  - ray is scattered at 900 with respect to the incident direction, the kinetic energy of the recoiling electron is given by (a) 378 KeV

Q72.

(b) 0.295 KeV

(d) 0.511MeV

(c) 0

The commutator of  px , f  x   is equal to

(a) i

(b) i

f  x  x

(c) i

f  x  x

(d) i f  x 

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fiziks Q73.

Institute for NET/JRF, GATE, IIT‐JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics    The value of the flux density for a wave function of the form

  x   Aeikx  Be ikx is

Q74.





(b)

 2 2 A B m





(d)

  A * B  B * A 2m

(a)

k 2 2 A B m

(c)

k 2 2 A B m





Te ground state wave function of a particle in a three-dimensional potential is given by

  r   Ae ar , where A is the normalization constant. The value of A is given by 3

  (a)    2  Q75.

3/ 4

 2  (b)     

1/ 2

  (c)    

3/ 4

  (d)    2 

3/ 2

The uncertainty product x.px for a one-dimensional simple harmonic oscillator is (a) equal to 

(b) greater than  / 2

(c) less than  / 2

(d) equal to  / 2

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