AIEEE 2009 - Physics

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PART-C : PHYSICS

61. Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate.

Assume that the duration of collision is negligible and the collision with the plate is totally elastic.

Then the velocity as a function of time and the height as a funciton of time will be :

1)

1+

1

t

t

y

ho

2)

1+

1

t

t

y

ho

1t12t

13t14t

3)t

t

y

h

1t 12t 13t 14t

4) t

t

y

h

o

1

Sol : 2

[CODE-B]


2/19





62. The height at which the acceleration due to gravity becomes9

g(whereg= the acceleration

due to gravity on the surface of the earth) in terms of R, the radius of the earth, is :

1)2

R2) / 2R 3) 2 R 4) 2R

Sol : 4

2gh R

g R h

= +

2

9

g R

g R h

= +

3R R h = +

2h R = .

63. A long metallic bar is carrying heat from one of its ends to the other end under steady-state.

The variation of temperature along the lengthx of the bar from its hot end is best describedby which of the following figures ?

1)

x

2)

x

3)

x

4)

x

Sol : 1

dQ dQKA

dt dx=

1 dQdQ dx

KA dt

=

.dQ dx


3/19





64. Two points P and Q are maintained at the potentials of 10V and -4V, respectivley. The work

done in moving 100 electrons from P to Q is :

1) 179.60 10 J 2) 162.24 10 J 3) 162.24 10 J 4) 179.60 10 J

Sol : 3

( )q V =

19100 1.6 10 (10 4)= +

1714 1.6 10=

162.24 10 .J=

Directions : Question number 65 and 66 are based on the following paragraph.

A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs

BC (radius = b) and DA (radius = a) of the loop are joined by two straight wires AB and CD. A

steady current I is flowing in the loop. Angle made by AB and CD at the origin O is 30.

Another straight thin wire with steady current1I flowing out of the plane of the paper is kept at

the origin.

B

I

C

D

O

Aa

b

301I

65. The magnitude of the magnetic field (B) due to the loop ABCD at the origin (O) is :

1)0 ( )

24

I b a

ab

2)

0

4

I b a

ab

3)0 2( ) ( )

4 3

Ib a a b

+ + 4) Zero

Sol : 1

net AD BC B B B= +G G

0 1 1

4 6

I

a b

=

0 ( )

24

I b a

ab

= .


4/19





66. Due to the presence of the current 1I at the origin :

1) The forces on AD and BC are zero.

2) The magnitude of the net force on the loop is given by1

0 2 ( ) ( )4 3

I Ib a a b

+ +

3) The magnitude of the net force on the loop is given by0 1 ( ).

24

I Ib a

ab

4) The forces on AB and DC are zero.

Sol : 1

Everywhere AD and BC, magnetic filed due to1I is tangential, hence force on them.

Directions : Question numbers 67, 68 and 69 are based on the following paragraph.

Two moles of helium gas are taken over the cycle ABCDA, as shown in the P-T diagram.

B

CD

300 K T

T

500 K

A

5101

5102

P (Pa)

67. Assuming the gas to be ideal the work done on the gas in taking it from A to B is :

1) 300 R 2) 400 R 3) 500 R 4) 200 R

Sol : 2

2 200 400 .nRdT R R = = =

68. The work done on the gas in taking it from D to A is :

1) +414 R 2) -690 R 3) +690 R 4) -414 R

Sol : 4

1

2

logenRT

=

2 300 log 2.eR=

414 .R=


5/19





69. The net work done on the gas in the cycle ABCDA is :

1) 276 R 2) 1076 R 3) 1904 R 4) Zero

Sol : 1

Total AB BC CD DAW W W W W = + + +

( )AB CDW W=

2 1(500) (300) ln

1 2nR nR

= +

(200) ln2nR=

2 200 0.693R=

= 276 R.

70. In an experiment the angles are required to be measured using an instrument. 29 divisions of the

main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of

the main scale is half-a-degree (= 0.5), then the least count of the instrument is :

1) half minute 2) one degree

3) half degree 4) one minute

Sol : 4

30 29 .VSD MSD=

291 .

30VSD MSD=

29(0.5 ).

30=

Least count 0.1 1MSD VSD=

29

0.5 1 30

=

10.5

30

=

1 60'1'

60 60= = =


6/19





71. A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each

of the other two corners. If the net electrical force on Q is zero, then Q/q equals :

1) -1

2) 1

3)1

2

4) 2 2

Sol : 4

72. One kg of a diatomic gas is at a pressure of 4 28 10 / .N m The density of the gas is 34 / .kg mWhat is the energy of the gas due to its thermal motion ?

1) 45 10 J

2) 46 10 J

3) 47 10 J

4) 43 10 J

Sol : 1

31

4

MV m

V= =

2

fU nRT =

2

fPV=

45 18 102 4=

45 10 .J=


7/19





73.

L

E

S

1R

2R

An inductor of inductance L = 400 mH and resistors of resistances1 2R = and 2 2R = are

connected to a battery of emf 12 V as shown in the figure. The internal resistance of the

battery is negligible. The switch S is closed at t = 0. The potential drop across L as a funciton

of time is :

1)312 te V

t

2)0.26 1

t

e V

3) 512 te V

4) 56 te V

Sol : 3

Max. current through L,2R branch.

0

126

2V A= =

Time constant3400 10

.2

Ls

R

= = = 0.2s

0.20 0[1 ] [1 ]

tRt

LV V e V e

= =

50

0.2

tVdV edt

=

emf.3 56400 10 10

2

tdVe L edt

= =

512 te e= .


8/19





This question contains Statement-1 and Statement-2. Of the four choices given after thestatements, choose the one that best describes the two statements.

74. Statement -1 : The temperature dependence of resistance is usually given as0R R= (1 ).t+

The resistance of a wire changes from 100 to 150 when its temperature is increased from

27 C to 227C. This implies that 32.5 10 / .C =

Statement - 2 :0R R= (1 )t+ is valid only when the change in the temperature T is

small and0 0( ) .R R R R =


9/19





3590

4= 442.5 .nm=

77. A particle has an initial velocity of 3 4i j+ and an acceleraiton of 0.4 0.3 .i j+ Its speed after10s is :

1) 7 2 units 2) 7 units

3) 8.5 units 4) 10 units

Sol : 1

78. The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejectedphotoelectrons was found to be 1.68 eV. The work function of the metal is : (hc = 1240 eV.nm)

1) 1.41 eV 2) 1.51 eV

3) 1.68 eV 4) 3.09 eV

Sol : 1

From Photo electric equation.

0

124001.68

4000W= +

0 1.41W eV =

79. Three sound waves of equal amplitudes have frequencies (v - 1), v, (v +1). Theysuperpose to

give beats. The number of beats produced per second will be :

1) 3 2) 2 3) 1 4) 4

Sol : 3

80. A motor cycle starts from rest and accelarates along a straight path at 22 / .m s At the starting

point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone

when the driver hears the frequency of the siren at 94% of its value when the motor cycle was

at rest ? (Speed of sound 1330 )ms=

1) 98 m 2) 147 m 3) 196 m 4) 49 m

Sol : 1

033094

100 330

V=

10 19.8V ms

=

Using 20 2 .V as=

98S m= .


10/19





81. BC D E

M

FA

bE

The above is a plot of binding energy per nucleon ,bE against the nuclear mass M; A, B, C, D,E, F correspond to different nuclei. Consider four reactions :

(i) A B C+ +

(ii) C A B + +

(iii) D E F+ +

(iv) F D E + +

where is the energy released ? In which reactions is positive ?

1) (i) and (iii)

2) (ii) and (iv)

3) (ii) and (iii)

4) (i) and (iv)

Sol : 4


11/19





82. A transparent solid cylindrical rod has a refractive index of2

.3

It is surrounded by air. A light

ray is incident at the mid-point of one end of the rod as shown in the figure.

The incident angle for which the light ray grazes along the wall of the rod is :

1)1 3sin

2

2)1 2sin

3

3)1 1sin

3

4)1 1

sin2

Sol : 3

CB

1 3sin ; 60

2C C= = =

90 60 30 .B = =

sin sinair h B =

2 1sin sin30 .

3 3 = =

1 1sin .3

=


12/19





83. Two wires are made of the same material and have the same volume. However wire 1 has

cross-sectional area A and wire 2 has corss-sectional area 3A. If the length of wire 1 increases

by x on applying force F, how much force is needed to stretch wire 2 by the same amount ?

1) 4F 2) 6F

3) 9F 4) F

Sol : 3

1 2 2

1 1 2 2

4F F lY

A e A e= =

Since volume of wires is same.

1 1 1 2 .A l A l=

2

2 1

4 33.

A A

l A A= = =

2 2 2

1 2 1 1

4F A e

F l A e =

2 33F A x

F A x

=

2 9 .F F=


13/19





This question contains Statement-1 and Statement-2. Of the four choices given after the

statements, choose the one that best describes the two statements.

84. Statement -1 : For a charged particle moving from point P to point Q, the net work done by an

electrostatic field on the particle is independent of the path connecting point P to point Q.

Statement - 2 : The net work done by a conservative force on an object moving along a closed

loop is zero.

1) Statement -1 is true, Statement - 2 is true; Statement - 2 is the correct explanation of

Statement - 1.

2) Statement - 1 is true, Statement - 2 is true; Statement-2 is not the correct explanation of

Statement - 1.3) Statement - 1 is false, Statement - 2 is true.

4) Statement - 1 is true, Statement - 2 is false.

Sol : 1


14/19





85. The logic circuit shown below has the input waveforms A and B as shown. Pick out the

correct output waveform.

Y

A

B

Input A

Input B

Output is :

1)

2)

3)

4)


15/19





Sol : 4

( )Y A B= +

A B A B BA + )( BA +

1

0

0

1

1

0

0

1

0

1

0

1

0

1

0

1

1

0

0

1

1

0

1

0

1

0

1

0

0

1

1

1

0

1

1

1

0

0

0

1

0

0


16/19





86. If x, v and a denote the displacement, the velocity and the acceleration of a particle executing

simple harmonic motion of time period T, then, which of the following does notchange with

time?

1) /aT x 2) 2aT v+

3) /aT v 4) 2 2 2 24a T v+

Sol : 4

For S.H.M.

sin ( )x r t= +

cos( ).v r t= +

2 sin ( )a r t= +

2 2 2 2 2 2 4 2 2 2 2 24 sin ( ) 4 cos ( )a T v T r t r t + = + + +

22 2 2 2 2 2 2

2

4sin ( ) 4 cos ( )T r t r t

T

= + + +

2 2 2 2 24 [sin ( ) cos ( )]r t t= + + +

2 2 24 .r cont = =87. A thin uniform rod of length land mass m is swinging freely abut a horizontal axis passing

through its end. Its maximum angular speed is . Its centre of mass rises to a maximum hegithof :

1)1

6

l

g

2)

2 21

2

l

g

3)

2 21

6

l

g

4)

2 21

3

l

g

Sol : 3

max

21

2mgh I =

max

221

2 3

mlmgh =

2 2

max6

lh

g

= .


17/19





88. In an optics experiment, with the position of the object fixed, a student varies the position of a

convex lens and for each position, the screen is adjusted to get clear image of the object. A

graph between the object distance u and the image distance v, from the lens, is plotted using the

same scale for the two axes. A straight line passing through the origin and making an angle of

45 with thex-axis meets the experimental curve atP. The coordinates ofPwill be :

1) ,2 2

f f

2) ( , )f f

3) (4 , 4 )f f 4) (2 , 2 )f f

Sol : 4

Foru = 2f; v = 2f image

45

A

BP

u

v

(2 , 2 )f f

2 .f =

Co-ordinates of P ( 2f, 2f).


18/19





89. Ap-n junction (D) shown in the figure can act as a rectifier. An alternating current source (V)

is connected in the circuit.

R

D

V

The current (I) in the resistor (R) can be shown by :

1)

I

t

2)

I

t

3)

I

t

4)

I

t

Sol : 2

Half-wave rectifier output.


19/19





90. Let4

( )Q

P r rR

=

be the charge density distribution for a solid sphere of radius R and total

charge Q. For a point p inside the sphere at distance1r from the centre of the sphere, the

magnitude of electric field is :

1) 20 14

Q

r 2)2

1

404

Q r

R

3)

21

4

03

Q r

R

4) 0

Sol : 2

2

44

Qdq r r dr

R

=

1

3

4

0

4

rQ

q r dr R

=

41

4

4

4

rQ

R=

41

4

Qr

R=

0

. enclosedE ds

=v

42 1

1 40

14

Q rE r

R =

214

04

QE r

R

=

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AIEEE 2009 - Physics

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