IIT JAM -2015 (PHYSICS) - trajectoryeducation.com

TRAJECTORY EDUCATION

(1)

Section - A

1. The electric field of a light wave is given by ˆ ˆsin( ) sin .4

E E i t kz j t kz

The

polarization state of the wave is(A) Left handed circular (B) Right handed circular(C) Left handed elliptical (D) Right handed elliptical(a) A (b) B(c) C (d) D

Ans. (c)The given wave is super position of two plane polarized wave with field vibration in pependicular

direction and phase difference of .4

The resulting wave will be elliptically polarized with field vibrating

in clockwise direction.Ey

Ex

2. The trace of a 2 × 2 matrix is 4 and its determinant is 8. If one of the eigenvalues is 2(1 + i), the othereigenvalues is(A) 2(1 + i) (B) 2(1 + i)(C) (1 + 2i) (D) (1 – 2i)(a) A (b) B(c) C (d) D

Ans. (a)The sum of eigenvalues is equal to trace and product of eigenvalues in called determinant. Othereigenvalues is 2 – 2i = 2(1 – i)

3. A mass m lying on a horizontal, frictionless, surface, is connected to one end of a spring. The other endof the spring is connected to a wall as shown in the figure. At t = 0 the mass is given an impulse

m Impulse

The time dependence of the displacement and the velocity of the mass (in terms of non-zero constantA and B) are given by(A) ( ) sin , ( ) cosx t A t v t B t (B) ( ) sin , ( ) sinx t A t v t B t

(C) ( ) cos , ( ) sinx t A t v t B t (D) ( ) cos , ( ) cosx t A t v t B t

IIT JAM -2015 (PHYSICS)


(2)

(a) A (b) B(c) C (d) D

Ans. (a)When mass m is given an impulse, the velocity will be finite and displacement will be zero at t = 0.

4. Temperature dependence of resistivity of a metal can be described by

(A) R

T

(B) R

T

(C) R

T

(D) R

T(a) A (b) B(c) C (d) D

Ans. (a)Resistivity of a metal increase with temperature.

5. A system consists of N number of particles, 1.N Each particle can have only one of the twoenergies E1 or 1 ( 0).E If the system is in equilibrium at a temperature T the average number ofparticles with energy E1 is

(A)2N

(B) / 1kT

Ne

(C) / 1kT

Ne

(D) /kTNe

(a) A (b) B(c) C (d) D

Ans. (a)Let the numbers of particles having energy E1 is n. So, number of particles in energy level 1E isN–nNumber of microstates

!!( )!

Nn N n

Entropy, S logk

!log!( )!

Nkn N n

[log ! log ! log( )!]k N n N n

( log ) ( log )k N N N n n n

[( ) log ( ) ( )]N n N n N n

(Using stirling approximation log ! logn n n n )


(3)

log log ( ) log ( )k N N n n N n N n In equilibrium,

dSdn =0

1 10 log log ( ) ( ) 0

( )k n n N n N n

n N n

[log( ) log ] 0k N n n

2NN n n n

6. At room temperature, the speed of sound in air is 340 m/sec. An organ pipe with both ends open has alength L = 29 cm. An extra hole is created at the position L/2. The lowest frequency of sound producedis(A) 293 Hz (B) 586 Hz(C) 1172 Hz (D) 2344 Hz(a) A (b) B(c) C (d) D

Ans. (c)There must be antinode at the open end. Since a hole has been made at the position L/2, So, there must

exist an antinode at .2Lx

L

2Lx

For lowest frequency, =L=29cm

Frequence of sound produced fV340 1172Hz0.29

7. A proton from outer space is moving towards earth with velocity 0.99c as measured in earth’s frame.A spaceship, travelling parallel to the proton, measure proton’s velocity to be 0.97c. The approximatevelocity of the spaceship, in the earth’s frame is(A) 0.2c (B) 0.3c(C) 0.4c (D) 0.5c(a) A (b) B(c) C (d) D

Ans. (d)


(4)

S S( )p

Let S be a frame attached to earth and S' be a frame attached to spaces ships.

xV 21

x

x

V VVV

c

0.97C2

0.990.991 x

c VV c

c

0.97c – 0.97 × 0.99V =0.99c–V V =0.5c

8. A particle with energy E is incident on a potential given by

V(x) =0 0

0x

V x

The wave function of the particle for E < V°. in the region x > 0 (in terms of positive constants A, B andk) is(A) Aekx + Be–kx (B) Ae–kx

(C) Aeikx + Be–ikx (D) zero(a) A (b) B(c) C (d) D

Ans. (b)

EV°

9. Consider the coordinate transformation , .2 2

x y x yx y The relation between the area elements

dx'dy' and dxdy is given Jdxdy. The value of J is(A) 2 (B) 1(C) –1 (D) –2(a) A (b) B(c) C (d) D

Ans. (c)

J( , )( , )x yx y

1 12 2 1

1 12 2

x xx yy yx y

10. A charge q is at the center of two concentric spheres. The outward electric flux through the inner


(5)

sphere is while that through the outer sphere is 2 . The amount of charge contained in the regionbetween the two spheres is(A) 2q (B) q(C) –q (D) –2q(a) A (b) B(c) C (d) D

Ans. (b)Gauss Law of electrostatics

q

q

11. A Zener regulator has an input voltage in the range 15V-20V and a load current in the range of5mA-20mA. If the Zener voltage is 6.8V, the value of the series resistor should be

15-20V+

–6.8V

6.8V°

Rz

(A) 390 (B) 420(C) 440 (D) 460(a) A (b) B(c) C (d) D

Ans. ()

12. The variation of binding energy per nucleon with respect to the mass number of nuclei is shown in thefigure

Consider the following reactions :

(1) 238 20692 82 10 22U Pb p n (2) 238 206 4

92 82 28 6U pb He e Which one of the following statements is true for the given decay modes of 238

92 ?U(A) Both (1) and (2) are allowed (B) Both (1) and (2) are forbidden(C) (1) is forbidden and (2) is allowed (D) (1) is allowed and (2) is forbidden(a) A (b) B(c) C (d) D

Ans. (d)(2) is forbidden because spin is voilated.

13. A satellite moves around the earth in a circular orbit of radius R centered at the earth. A secondsatellite moves in an elliptic orbit of major axis 8R, with the earth at one of the foci. If the former takes1 day to complete a revolution, the latter would take


(6)

(A) 21.6 days (B) 8 days(C) 3 hours (D) 1.1 hour(a) A (b) B(c) C (d) D

Ans. (b)2 3T a

when a is length of semi major axis.

Time period of revolution of latter is 64 days = 8 days.14. A hollow, conducting spherical shell of inner radius R1 and outer radius R2 encloses a charge q inside.

Which is located at a distance d(< R1) from the centre of the sphare. The potential at the centre of theshell is

q d

R1

R2

(A) Zero (B)1

4qd

(C)1

14

q qd R

(D)

1 2

14

q q qd R R

(a) A (b) B(c) C (d) D

Ans. (b)

Potential at centre of shell4

qVd

+

+

+

+

+

+

+

+

+

+

+

++++

+

+

+

+

+

+

+

+

+–

–

–

–

–

–

–

–

–

–

–

––––

–

–

–

–

–

–

–

–

–+

+

++++

+++

+

+ +–

–

–––

–––

– –

– ––

–––

––––

qqq

q –q

15. Vibrations of diatomic molecules can be represented as those of harmonic oscillators. Two halogenmolecules X2 and Y2 have fundamental vibrational frequencies vx = 16.7 × 1012 Hz and vy = 26.8 × 1012

Hz, respectively. The respective force constants are kX = 325 N/m and kY = 446 N/m. The halogenmolecules X2 and Y2 are(A) X2 = F2 and Y2 = Cl2 (B) X2 = Cl2 and Y2 = F2(C) X2 = Br2 and Y2 = F2 (D) X2 = F2 and Y2 = Br2(a) A (b) B(c) C (d) D

Ans. (b)


(7)

m m

v =1

2k

X

Y

vv = . . .X Y X Y X Y

Y X Y X Y X

k k m k Mk k m k M

12

12

16.7 1026.8 10

=325446

Y

X

MM

Y

X

MM =0.533

16. A rigid and thermally isolated tank is divided into two compartments of equal volume V, separated by athin membrane. One compartment contains one mole of an ideal gas A and the other compartmentcontains one mole of a different ideal gas B. The two gases are in thermal equilibrium at a temperatureT. If the membrane ruptures, the two gases mix. Assume that the gases are chemically inert. Thechange in the total entropy of the gases on mixing is(A) 0 (B) R ln2

(C)3 ln 22

R (D) 2R ln 2

(a) A (b) B(c) C (d) D

Ans. (d)17. A system comprises of three electrons. There are three single particle energy levels accessible to each

of these electrons. The number of possible configuration for this system is(A) 1 (B) 3(C) 6 (D) 7(a) A (b) B(c) C (d) D

Ans. (a)18. Doppler effect can be used to measure the speed of blood through vessels. Sound of frequency 1.0522

MHz is sent through the vessels along the direction of blood flow. The reflected sound generates a beatsignal of frequency 100 Hz. The speed of sound in blood is 1545 m/sec. The speed of blood through thevessels, in m/sec is(A) 14.68 (B) 1.468(C) 0.1468 (D) 0.01468(a) A (b) B(c) C (d) D

Ans. (c)Let v be the speed of blood in vessel and v° be the speed of sound in air

v° + v =1545 ...(1)Also from Doppler effect

VvV V

=v

V

V V

=

1.05221.0521


(8)

VV =

1.05220.0001

v°=10522 vPutting v° = 10522v in equation (1) we get, v = 0.1468 m/s.

19. A positively charged particle, with a charge q, enters a region in which there is a uniform electric field

E

and a uniform magnetic field B both directed parallel to the positively y-axis. As t = 0, the particle

is at the origin and has a speed v0 directed along the positive x-axis. The orbit of the particle projectedon the x-z plane is acircle.Let T be the time taken to complete one revolution of this circle. The y-coordinate of the particle at t = T is given by

(A)2

22mE

qB

(B)2

2

2 mEqB

(C)2

2

mE v mqB qB

(D)

22 mvqB

(a) A (b) B(c) C (d) D

Ans. (b)y

xv°

E B

z

The path travelled by particle is helix along y-axis

qvB =2mv

R

=v qBR m

Time period, T=2 2 m

qB

ay =qEm

y =2 2

22 2

1 1 4. .2 2y

qE ma tm q B

=2

2

2 mEqB

20. A rigid triangular molecule consists of three non-collinear atoms joined by rigid rods. The constantpressure molar specific heat (Cp) of an ideal gas consisting of such molecules is(A) 6R (B) 5R(C) 4R (D) 3R(a) A (b) B(c) C (d) D


(9)

Ans. (c)

Cv =2fR

where f is degree of freedomFor rigid triangular molecule, f = 6So, Cv =3R

Cp= Cv + R = 4R21. A conducting wire is in the shape of a regular hexagon which is inscribed inside an imaginary circle of

radius R, as shown. A current I flows through the wire. The magnitude of the magnetic field at thecentre of the circle is

IR

C

(A)3

2I

R

(B) 2 3I

R

(C)3 I

R

(D)

32

IR

(a) A (b) B(c) C (d) D

Ans. (c)Magnetic field due to each side

RR 30°

30°

B1 = sin sin4

Id

= sin30 sin304 cos30

IR

= tan302

IR

Total magnetic field, B =6B

=3 I

R


(10)

22. Consider the equation2dy y

dx x with the boundary condition y(1) = 1. Out of the following the range of

x in which y is real and finite is(A) 3x (B) 3 0x (C) 0 3x (D) 3 x (a) A (b) B(c) C (d) D

Ans. (d)dydx =

2yx

2

dyy =

dxx

1

y

=logx + c

y(1) =1

1y =1 – logx

y=1

1 log x

log x is defined for 0x y goes to infinity for logx = 1 x = 2.71e So, y is real and finite for 3 .x

23. An observer is located on a horizontal circular turntable which rotates about a vertical axis passingthrough its center, with a uniform angular speed of 2 rad/sec. A mass of 10 grams is sliding withoutobserved to move towards the center with a speed of 6cm/sec. The net force on the mass, as seen bythe observer at that instant is(A) 0.0024 N (B) 0.0032 N(C) 0.004 N (D) 0.006 N(a) A (b) B(c) C (d) D

Ans. (c)Centrifugal force Fcfg = ( )m r

|Fcfg| =2m r in radially outward direction

=0.01 × 4 × 0.08 = 0.0032N

Coriolis force, corrF

= 2m v

Fcorr

Fcfgv


(11)

corrF

= 2m v

=2 × 0.01 × 2 × 0.06=0.0024 N

Net force F = 2 2corrcfgF F

=0.004 N24. Seven uniform disks, each of mass m and radius r, are inscribed inside a regular hexagon as shown.

The moment of inertia of this system of seven disks about an axis passing through the central disk andperpendicular to the plane of the disks, is

(A) 272

mr (B) 7mr2

(C) 2132

mr (D) 2552

mr

(a) A (b) B(c) C (d) D

Ans. (d)

Using parallel axes theorem I =2 2

26 (2 )2 2

mr mr m r

=27.5 mr2 = 2552

mr

25. The fourier series for an arbitrary periodic function with period 2L is given by

1 1( ) cos sin .2 n n n na n x n xf x a b

L L

For the particular periodic function shown in the figure

the value of a° is

1

1/2

f x( )

1 2–2 –1 0x

(A) 0 (B) 0.5(C) 1 (D) 2(a) A (b) B(c) C (d) D

Ans. (d)26. The phase of the complex number (1 + i)i in the polar representation is

(A) / 4 (B) / 2


(12)

(C) 3 / 4 (D) 5 / 4(a) A (b) B(c) C (d) D

Ans. (c)z = i + i2

=–1 + i= 3 /42 ie

Phase of z is 3 .4

27. Which of the following circuits represent the Boolean expression

S P QR QP

(A) PQ

S(B) P

QS

(C) PQ

RS

(D) PQ

RS

(a) A (b) B(c) C (d) D

Ans. (b)

S = P QR QP

= ( )( )P QR QP

PQ

S

= ( )( )P QR QP

= PQP QQRP

= PQ

28. Consider a vector field 3 ˆˆ ˆ .F yi xz j zyk

Let C be the circle x2 + y2 = 4 on the plane z = 2, oriented

counter clockwise. The value of the contour integral .C

F dr is

(A) 28 (B) 4(C) 4 (D) 28 (a) A (b) B(c) C (d) D

Ans. (a)

.c

F dr

= 3ydx xz dy zydz = 8ydx xdy

(z = 2, dz = 0)


(13)

=2

0

2sin .( 2sin ) 8 2cos .cos 2cosd d

=2

2 2

0

( 4sin 32cos ) d

= 28

29. Miller indices of a plane in cubic structure that contains all the directions [100], [011] and [111] are(A) (011) (B) (101)(C) (100) (D) (110)(a) A (b) B(c) C (d) D

Ans. (a)30. A nucleus has a size of 10–15 m . Consider an electron bound within a nucleus. The estimated energy of

this electron is of the order of(A) 1 MeV (B) 102 MeV(C) 104 MeV (D) 106 MeV(a) A (b) B(c) C (d) D

Ans. (d)According to Heisenberg uncertainty principle

p–34

1915

6 10 6 1010r

kE2 –38

731

36 10 6 102 2 9.1 10pm

610 MeVSection - B

1. The following figure shows a double slit Fraunhofer diffraction pattern produced by two slits, each ofwidth a, separated by a distance b, a < b. Which of the following statements are correct?

Secondary maxima

Primary maxima(A) Reducing a increases the separation between consecutive primary maxima(B) Reducing a increases the separation between consecutive secondary maxima(C) Reducing b increases the separation between consecutive primary maxima(D) Reducing b increases the separation between consecutive secondary maxima(a) A (b) B(c) C (d) D

Ans. (a, b, d)Position of primary maxima are given by

1 1 11.43 2.462 3.4710,sin ,sin ,sina a a

position of secondary maxima are given by


(14)

n = 1sin na b

So, reducing a, increases seperation between consecutive primary maxima as well secondary maximaand reducing b increases the seperation between secondary maxima only

2. In an ideal Op-Amp circuit shown below. 1 23 , 1R k R k and 0.5(sin ).iV t Which of thefollowing statements are true?

P

V1 V0

R1

R2

+–

(A) The current through R1 = The current through R2

(B) The potential at P is2

1

RR

(C) The amplitude of V° is 2V(D) T h e o u t p u t v o l t a g e V° is in phase with Vi(a) A (b) B(c) C (d) D

Ans. (a, c, d)Vp =Vi

P

V1 V°

R1

R2

+–

i

i

current i =2 2

p iV VR R

V° =Vp + iR1

= 1

2i i

RV VR

=1

2

1 4i iR V VR

= 2sin t3. A particle is moving in a two-dimensional potential well

( , ) 0 0 ,0 2elsewhere

V x y x L y L

Which of the following statements about the ground state energy E1 and ground state eigenfunction


(15)

are true?

(A)2 2

1 2EmL

(B)2 2

1 2

58

EmL

(C)2 sin sin

2x y

L L L

(D)2 cos cos

2x y

L L L

(a) A (b) B(c) C (d) D

Ans. (b, c)

x yn n = 2 sin sin2yx n yn x

L L L

x yn nE =22 2 2

2 22 4yx nn

m L L

Ground state energy

E1 =2 2

2

58mL

(nx = 1, ny = 1)

Ground state eigenfunction

11 =2 sin sin

2x y

L L L

4. A unit cube made of a dielectric material has a polarization ˆ ˆ3 4P i j

units. The edges of the cubeare parallel to the Cartesian axes. Which of the following statements are true?(A) The cube carries a volume bound charge of magnitude 5 units(B) There is a charge of magnitude 3 units on both the surfaces parallel to the y-z plane(C) There is a charge of magnitude 4 units on both the surfaces parallel to the x-z plane(D) There is a net non-zero induced charge on the cube(a) A (b) B(c) C (d) D

Ans. (b, c)Apply Boundary condition, P2n – P2n = b

5. A rod is hanging vertically from a pivot. A particle traveling in horizontal direction collides with the rodas shown in the figure. For the rod particle system consider the linear momentum and the angularmomentum about the pivot. Which of the following statements are NOT true?

(A) Both linear momentum and angular momentum are conserved(B) Linear momentum is conserved but angular momentum is not(C) Linear momentum is not conserved but angular momentum is conserved(D) Neither linear momentum nor angular momentum are conserved(a) A (b) B(c) C (d) D

Ans. (c)6. A particle of mass m is moving in x-y plane. At any given time t, its position vector is given by

ˆ ˆ( ) cos sin .r t A ti B tj where A, B and are constants with .A B Which of the following


(16)

statements are true?(A) Orbit of the particle is an ellipse(B) Speed of the particle is constant(C) At any given time t the particle experiences a force towards origin

(D) The angular momentum of the particle is ˆm ABk(a) A (b) B(c) C (d) D

Ans. (a, c, d)

V

= ˆ ˆsin cosdr A ti B tjdt

L

= r mv

=

ˆˆ ˆ

cos sin 0sin cos 0

i j km A t B t

A t B t

= ˆm ABk7. As shown in the P-V diagram, AB and CD are two isotherms at temperatures T1 and T2 respectively

(T1 > T2). AC and BD are two reversible adiabats. In this cannot cycle, which of the following statementsare true?

F A

B

CD

Q1

Q2

T1

T2

v

(A)1 2

1 2

Q QT T (B) The entropy of the source decreases

(C) The entropy of the system increases (D) Work done by the system W = Q1 – Q2(a) A (b) B(c) C (d) D

Ans. (a,b, d)8. Consider the circuit, consisting of an AC function generator ( ) sin 2V t V vt with V° = 5V, an inductor

L = 8.0mH, resistor 5R and a capacitor 100 .C F Which of the following statements are true ifwe vary the frequency?


(17)

R C

L

(A) The current in the circuit would be maximum at v = 178Hz(B) The capacitive reactance increases with frequency(C) At resonance, the impedance of the circuit is equal to the resistance in the circuit(D) At resonance, the current in the circuit is out of phase with the source voltage(a) A (b) B(c) C (d) D

Ans. (a, c)

v = –3 –6

1 1 1 12 2 8 10 100 10LC

=178Hz9. For an electromagnetic wave travelling in free space, the electric field is given by

8 ˆ100(10 ) / .E t kx JV m

Which of the following statements are true?(A) The wavelength of the wave in meter is 6(B) The corresponding magnetic field is directed along the positive z direction(C) The Polynting vector is directed along the positive z direction(D) The wave is linearly polarized(a) A (b) B(c) C (d) D

Ans. (a, d)

c =810

k k

y

x

EH

z�n

k =82 10

c

= 6

10. Muons are elementary particles produced in the upper atmosphere. They have a life time of 2.2 .sConsider muons which are traveling vertically towards the earth’s surface at a speed of 0.998c. For anobserver on earth, the height of the atmosphere above the surface of the earth is 10.4 km. Which of thefollowing statements are true?(A) The muons can never reach earth’s surface(B) The apparent thickness of earth’s atmosphere in muon’s frame of reference is 0.96 km(C) The lifetime of muon in earth’s frame of reference is 34.8 s


(18)

(D) Muons traveling at a speed greater than 0.998c reach the earth’s surface(a) A (b) B(c) C (d) D

Ans. (c, d)Life time of muon in earth’s frame of reference

= 2 2

2

2.2 34.81 0.9981

svc

Apparent thickness of earth’s atmosphere in muon’s frame of reference

=2

221 10.4 1 0.998 0.657v km

c

Section - C1. A rod is moving with a speed of 0.8c in a direction at 60° to its own length. The percentage contraction

in the length of the rod is __________.Ans.

Component of velocity parallel to rodv =0.8c.cos60°

=0.4c

=2

221 1 0.4v

c

=0.9165 Percentage contraction = 91.65

2. GaAs has a diamond structure. The number of Ga-As bonds per atom which have to be broken tofracture the crystal in the (001) plane is ___________.

Ans. 4

3. X-rays of wavelength 0.24 nm are Compton scattered and the scattered beam is observed at an angleof 60° relative to the incident beam. The compton wavelength of the electron is 0.00243 nm___________.

Ans. = (1 cos )c

= 0.0012152

c nm

= 0.241215nm kE of scattered electron

kE =hc hc

=26eV4. A particle is in a state which is a superposition of the ground state and the first excited state 1 of

a one-dimensional quantum harmonic oscillator. The state is given by 11 2 .2 5

Ans.

E =1 4 35 2 3 2


(19)

= 1.3 5. The power radiated by sun is 3.8 × 1026 W and its radius is 7 × 105 km. The magnitude of the Poynting

vector (in W/cm2) at the surface of the sum is _____________.Ans.

Poynting vector, S = 24Pr

=26

20

3.8 104 3.14 49 10

=6174W/cm2

6. In an experiment on charging of an initially uncharged capacitor, an RC circuit is made with theresistance 10R k and the capacitor 1000C F along with a voltage source of 6V. The magnitudeof the displacement current through the capacitor (in ),A 5 seconds after the charging has started is_____________.

Ans.Displacement Current =Conduction current

i = /t RCeR

= 5/103

610 10

e

=363.9 A7. In the given circuit, Vcc = 10V and 100 for the n-p-n transistor. The collector voltage Vc (in volts) is

_____________.VCC

1 K

VC100 K

5V+–

Ans.VB – 100IB =0

IB =5 0.7 43

100A

IC =BIB = 100 × 0.043 = 4.3mAVC=VCC – ICRC

=10 – 4.3 × 1 = 5.7 V8. A diode at room temperature (kT = 0.025 eV) with a current of 1 A has a forward bias voltage

VF = 0.4V. For VF = 0.5V, the value of the diode current (in )A is _______________.Ans.54.6

9. In the hydrogen atom spectrum, the ratio of the longest wavelength in the Lyman series (final state


(20)

n = 1) to that in the Balmer series (final state n = 2) is ___________.Ans.

1 1Longest Wavelength of LymanSeries 4 9= 1Longest Wavelength of BalmerSeries 1

4

=5 0.18518527

10. Unpolarized light is incident on a calcite plate at an angle of incidence 50°, as shown in the figure. Taken0 = 1.6584 and ne = 1.4864 for calcite. The angular separation (in degrees) between the two emergentrays within the plate is _____________.

Calcite

AirO

ptic

axis

Ans.

r = 1 sinsin i

n

For ordinary light, 1 = 1 0.707sin 28.041.6584

For extraordinary light, 2 = 1 0.707sin 31.561.4864

Angular seperation = 2 1 3.52 11. A nozle is in the shape of a truncated cone, as shown in the figure. The area at the wide end is 25 cm2

and the narrow end has an area of 1 cm2. Water enters the wider end at a rate of 500 gm/sec. Theheight of the nozzle is 50 cm and it is kept vertical with the wider end at the bottom. The magnitude ofthe pressure difference in kPa (1kPa = 103 N/m2) between the two end of the nozzle is _________.

50 cm

Ans.

21 1

12

P v = 22 1

12

P v gh


(21)

2

1

P1 – P2 = 2 22 1

1 12 2

v v gh

=2

2 2

2 2 2 21

1 12 2

Q Q ghA A

=2 2

33 8 3 8

1 0.5 1 0.5 10 10 0.52 10 10 2 10 625 10

=17.48 kPA

12. In a region of space, a time dependent magnetic field B(t) = 0.4t Tesla points vertically upwards.Consider a horizontal, circular loop of radius 2 cm in this region. the magnitude of the electric field (inmV/m) induced in the loop is _______________.

Ans.

.E dl

= ˆ.B ndSt

.2E r = 2(0.4 )d t rdt

E =1 0.4 0.02 4 /2

mV m

13. Consider a 20 m diameter p-n junction fabricated in silicon. The donor density is 1016 per cm3. Thecharge developed on the n-side is 1.6 × 10–13 C. Then the width (in )m of the depletion region on then-side of the p-n junction is _______________.

Ans.14. For the arrangement given in the following figure, the coherent light sources. A, B and C have individual

intensities of 2mW/m2 and 5 mW/m2, respectively at point P. The wavelength of each of the sources is600 nm. The resultant intensity at point P (in mW/m2) is _____________.

3.22 mm

2.04 mm

A

B

CAns.

Let Wave emerging from A, B & C are 1 2 3, &


(22)

Phase difference between 1 2&

–3–9

2 2 1.52 sin 3.22 10600 10 100

d

= 161So, 1 2& are out of phase. Hence, 1 2 0

So, the intensity at P is only due to 3I =5mW/m2

15. A block of mass 2kg is at rest on a horizontal table. The coefficient of friction between the block andthe table is 0.1. A horizontal force 3N is applied to the block. The speed of the block (in m/s) after it hasmoved a distance 10m is ______________.

Ans.Friction force, f = mg

=0.1 × 2 × 10 = 2N

2kg 3N

Net force acting towards right is 1N and hence acceleration is 0.5m/s2

Speed of block after it moves a distance of 10m isv = 2 2 0.5 10 3.16 /as m s

16. A plane electromagnetic wave of frequency 5 × 1014 Hz and amplitude 103 V/m traveling in ahomogeneous dielectric medium of dielectric constant 1.69 is incident normally at the interface with asecond dielectric medium of dielectric constant 2.25. The ratio of the amplitude of the transmittedwave to that of the incident wave is ______________.

Ans.1.1417. A homogeneous semi-circular plate of radius R = 3 m is shown in the figure. The distance of the center

of mass of the plate (in meter) from the point O is ______________.

O 3rnAns.

Yam =ydm

dm

x

d

y

= 0 0

0 0

sinR

R

r rdrd

rdrd


(23)

= 0

0

sin2 43 3

dRR

d

For R = 3m, Ycm =4 1.27m

18. One gram of ice at 0°C is melted and heated to water at 39°C. Assume that the specific heat remainsconstant over the entire process. The latent heat of fusion of ice is 80 Calories/gm. The entropychange in the process (in Calories per degree) is _______________.

Ans.

S =312

273

.273m L mcdT

T

=80 312ln 0.4266273 273

19. In the thermodynamic cycle shown in the figure, one mole of a monatomic ideal gas is taken through acycle. AB is a reversible isothermal expansion at a temperature expansion at a temperature of 800 Kin which the volume of the gas is doubled. BC is an isobaric contraction to the original volume in whichthe temperature is reduced to 300 K. CA is a7

\\\\\\\\\\\\\\\\\\\\\\\7\\\\\\

\\\

\\\| | |

| \

\] ] ] ] ] ] ] ] ] ] ]

Documents

IIT JAM -2015 (PHYSICS) - trajectoryeducation.com