12th Physics Em Compulsory Proplems

8/18/2019 12th Physics Em Compulsory Proplems

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WWW.KALVIKURAL.COM WWW.HAISTUDENTS.COM

1

My hearty congratulations to +2 Students!

If you want to get ‘200’ out of ‘200’ in Physics, you should

be answered the compulsory problem as well as possible. The

physics learners are advised to frame their own responses taking

ideas from the help – points given for each problem.

Here, All the public examination

questions (Up to Sep – 2015) particularly, Sixty Seven problems

are dealt in a detailed and simple manner, just like your attempts.The students are thus prepared in an effective way to face the

compulsory problem confidently and come out with flying colours.

With best wishes and regards,

Walk with educational service

T.Thamaraiselvan,

PGT Physics,

G.B.H.S. School,

Aranthangi – 614616

Cell: 9443645072

Email Id :

[email protected]

mailto:[email protected]:[email protected]:[email protected]


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1. A Parallel Plate capacitor has plates of area 200 cm2 and separation

between the plates 1mm. Calculate (i) The potential difference between the plates if 1 nc

charge is given to the capacitor (ii) with the same charge if the plate separation is

increased to 2mm, what is the new potential difference and ((iii) electric field between

the plates. [March: 2006]

A=200 cm2

=200 x 10-4m2

d = 1 x 10-3 m

(i) q = 1 x 10-9 c The potential difference between the plates v =? d q d

v = =0 A. 0

1 x 10-9 x 1 x 10-3 =

2 x 10-2 x 8.854x 10-12

v=5.65 v

(ii) If d

= 2 m m v

=?

If the distance increase by two times the P.D also will increase two times/v

= 2 x 5.65 =11.3 V

(iii) Electric Field E = v / d = 5.65 / 10-3

= 5650 v / m.

2. Three capacitors each of capacitance a 9 pF are connected in series (i) What is thetotal capacitance of the combination? (ii) What is the potential difference across eachcapacitor, if the combination is connected to 120V Supply?

[June - 2006, Sep 2006, June - 2011]Given

C = 9 pF v =120 v

n = 3 v1= v2= v3=?

Cs = ? v1= v2= v3=v / n = 120 / 3

CS = c/n = 9/3 v1= v2= v3=40 v

CS = 3 pF

1 cm = 10

-m


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3.Two Capacitances 0.5 F and 0.75 F are connected in parallel and the combination toa 110v battery. Calculate the charge from the source and charge on each capacitor?

Given: - [June - 2007]c1=0.5 F ; c2=0.75 Fv = 110 v

q1, q2=? Total Charge q = ? q1=c1 v= 0.5 x 10-6 x 110

q1= 55 cq2=c2 v

=0.75 x 10-6 x 110q2 =82.5 cq = q1+q2 =55+82.5q = 137.5 c

4. Calculate the electric potential at a point P, located at the centre of the square of point

charges shown in the figure [June- 2007]q1=12 nc ; q2=-24nc;q3=31 nc ; q4=17 nc D Cif a=1.3 m 17nc 31nc r=.OA ;=OB =OC=OD= a / 2 o

12nc -24 ncV = 1 [q1+ q2+q3+ q4] A B

40r 1.3 m= 9 x 109 x 2 12-24+31+17

1.39 x 1.414 x 36 x 10-9 x 109

V =1.3

V = 352.4 V


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5. Two positive charges of 12 C and 8C respectively are 10 cm apart. Find thework done in bringing them 4 cm Closer, so that, they are 6cm apart. [June 2008]

Given :- q1 =12 c; q2 =8cIf r 1=10 cm

9 x 109 x q1 q2

Intial Energy Ui = r 1

9 x 109 x 12 x 10-6 x 8 x 10-6 =

10 x 10-2

= 8.64 JIf r 2 = 6 cm /Final Energy

9 x 109 x 12 x 10-6 x 8 x 10-6 Uf =

6 x 10

-2

Uf = 14.4JWork Done = W = Uf-Ui

=14.4 – 8.64W= 5.76 J

6. Two capacitors of unknown capacitances are connected in series and parallel if the netcapacitances in the two combinations are 6 F and 25 F respectively find theircapacitances

[Sep 2008]Given :-Cp=25 F

Cs = 6 F: c1 , c2 =?Cp = c1 +c2/ c1 +c2 =25 F C2 =(25 – C1) F Cs = C1 C2 / C1+C2

C1 C2=6

C1+C2

C1 C2=6

25

C1 C2 = 150

C1 (25-C1) = 150

25C1 - C12 = 150

25C1 - C12 -150 = 0

C12 - 25C1 + 150 = 0

(C1 -15)(C1 -10) = 0

C1 = 15 (0r) 10

/C1 =15 F

C2 = 10 F


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7. The plates of parallel plate capacitor have an area of 90cm2 each and are separated by 2.5 mm. The capacitor is charged by connecting it is a 400V supply, how muchelectrostatic energy is stored by the capacitor? [June 2009, Sep 13]

A=90 cm2 = 90 x 10-4 m2

d=2.5 x 10

-3

mv=400 vE=?E=cv2/2

C=0A / d/ E =1 x 0A x v

2 2 d

1 8.854 x 10 -12 x 90 x 10 -4x 400 x 400E = x

2 2.5 x 10 -3

= 2.55 x 10-6

J

8. There Charges -2x10-9C, 3x10-9 C, -4x10-9 C are placed at the vertices of anequilateral triangle ABC of side 20 cm Calculate the work done in shifting the charges A,B and C to A1, B1, and C1 respectively which are the mid points of the sides of thetriangle. [June -2011]

AB=BC=AC=20 X 10-2 m A -2 x 10-9 Cq1 = -2 x 10

-9 C

q2 = 3 x 10-9 C

q3

= -4 x 10-9 C

U=?B B1

C3 x 10-9 C -4 x 10-9 C

Initial Potential Energy Ui = 1 / 40d [q1 q2 + q2 q3+ q3 q1 ]

9 x 109 [ ( -2 x 10-9 x 3 x 10-9 ) + ( 3 x 10-9 x -4 x 10-9 ) +Ui = ( -4 x 10-9 x -2 x 10-9 ) ]

20 x 10-2

9 x 109= [ ( -6 x 10-18-12 x 10-18+8 x 10-18]

20 x 10-2

-9 x 109 x 10 x 10-18

Ui = = 4.5x 10 -7 J20 x 10-2


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If the Charges on A, B, and C distance final potential energy r = 10 x 10-2 m

9 x 109

Uf= [-10 x 10-18]

10 x 10-2

=-9 x 10-7

J

/U=Uf-Ui = -9 x 10-7 – (-4.5 x 10-7)= -(9+4.5) x 10-7

U = -4.5 x 10-7 J

9. In the given network, calculate the effective resistance between points A and B .Find the effective resistance one unit [March: 2007]

/The network hasthree identical units

C D

R 1, R 2 are connected in seriesR s1=R 1+R 2 =5+10= 15Ω 5+10R 1sR 3, R 4 are connected in seriesR s2 = R 3+R 4 R s2 = 5+10= 15Ω R s1, R s2 are connected inParallel /Rp1 = R s / n = 15 / 2 =7.5 Ω

Each unit has a resistance of 7.5 Ω

R s = nRp = 3 x 7.5R s = 22.5 Ω

10. The effective resistances are 10Ω , 2.4 Ω when two resistors are connected in seriesand parallel. What are the resistances of individual resistors

[March : 2007, March : 2010 October -2011, March : 2015]

R s = 10Ω; R P =2.4 Ω; R 1,R 2=?R s= R 1+R 2R 1+R 2= 10Ω

R 2= (10- R 1)Ω R P = R 1 R 2 /( R 1+R 2)R 1R 2 / (R 1+R 2) = 2.4R 1R 2 / 10 =2.4R 1R 2=24

R 1 (10-R 1)=2410R 1 – R 1

2 -24=0

R 12 – 10 R 1+24=0

(R 1-6) (R 1-4)=0R 1= 6 or 4/ R 1= 6 Ω ; R 2= 4 Ω


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11. A copper wire of 10-6m2 area of cross section carries a current of 2A, if the number ofelectrons per cubic metre is 8 x 10 28, calculate the current density and average driftvelocity.( e=1.6 x 10-19 c) [March : 2009]

A=10-6 m2 ; I=2A; n=8 x 1028;e=1.6 x 10-19 cJ=? vd=?

J=I / A =2 / 10

-6

=2 x 10

6

A m

-2

J 2 x 106 vd= =

n.e 8 x 1028x1.6x10-19

=0.156 x 10-3

vd =1.56 x 10-4 ms-1

12. Three resistors are connected in series with 10V supply as shown in the figure.Find the voltage drop across each resistor [June - 2010 March: 2012]Effective resistance of series combination R s= R 1+R 2+R 3

R s= 5+3+2 = 10 Ω / Current in Circuit I=v/ R s=10/10 = 1 AVoltage drop across R 1 v1 =I R 1 = 1 x 5 =5 V Voltage drop acrosR 2 v2 =I R 2= 1 x 3 =3 V Voltage drop acrosR 3 v3 =I R 3 = 1 x 2 =2 V.

13. What is the drift velocity of an electron in a copper conductor having area10 x 10-6 m2 carrying a current of 2A. Assume that there are 10 x 1028 electrons /m3

[March : 2009]A = 10 x 10-6 m-2 ; I=2A; n=10 x 1028 electrons / m3

vd = ?I = n A e V

dVd = I / n A e= 2 / [10 x 1028 x 10 x 10-6 x 1.6 x 10-19]

Vd = 1.25 x 10-5 ms-1

14. Find the current flowing across the resistors 3 Ω, 5 Ω and 2 Ω connected in parallel to a 15 v supply, Also find the effective resistance and total current drawn fromthe supply [Oct-2010> March - 15]

R 1= 3 Ω ; R 2= 5 Ω; R 3= 2 Ω V=15 vI1,I2,I3 =?Total Current I =?Effective Resistance=?Current Through R 1 I1 = V / R 1 =15/3 = 5ACurrent Through R 2 I2 = V / R 2 =15/5 = 3A

Current Through R 3 I3 = V / R 3 =15/2 = 7.5A/ Total Current I = I1+I2+I3

= 5+3+7.5=15.5AEffective Resistance R = v / I =15 / 15.5

= 0.967 Ω


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15. In a metre bridge, the balancing length for a 10 Ω resistance in left gap is 51.8 cm.Find the unknown resistance and specific resistance of a wire of length 108 cm and radius0.2 mm.

[Oct-2010> June - 2010]

P = 10 Ω l1 = 51.8cml2 = 48.2cmQ = ?

Q / P = l2 / l1Q = P. l2 / l1 = 10 x 48.2 / 51.8Q=9.3 Ω

L = 108 cm = 1.08mr = 0.2 x 10-3 m = 2 x 10-4 m.=?= Q.A / L =>Q. r 2 / L

9.3 x 3.14 x (2 x 10-4

)2

= 1.08

= 108.2 x 10-8 =1.082 x 10-6 Ωm

16. An iron box of 400 W power is used daily for 30 minutes. If the cost per unit is 75 paise, find the weekly expense on using the iron box

[June - 2012]P=400 W; t=1/2 Hour.Rate /Unit = 75 Paise Cost /Week = ?

Energy consumed in one day = P x t = 400 x 1 / 2=200 w h

W =0.2 k whW =0.2 Unit

Energy consumed in one week =7 x 0.2=1.4 Unit

Cost / Week = Total units consumed x (rate / unit) = 1.4x0.75 = Rs.1.0517. The r esistance of a field coil measures 50 Ω at 20oC and 65 Ω at 70oC. Find thetemperature coefficient of resistance.t1= 20º C; R 1= 50 Ω, t2 = 70º C R 2= 65 Ω α =? [June 2013]

α = R 2-R 1 R 1t2-R 2 t1 = 65-50 = 15

(50x70) – (65x20) 3500-1300

= 15 = 0.0068 / º C2200


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18. A circular coil of radius 20cm has 100 turns wire and it carries a current of 5A.Find the magnetic induction at a point along its axis at a distance of 20cm from the centreof the coil. [March 2006, Oct -2006, March 2009,June-2015]

n =100 turns a = 20 x 10-2 m

I = 5 Ax = 20 x 10-2 mB =?

n0 Ia2

B =

2(a2 + x2 ) 3 / 2 102 x4 x 3.14 x 5 x 4 x10-2 x10-7

=

2(4 x 10-2 + 4 x 10-2) 3 / 2

4 x 3.14 x 10

-6

4 x 3.14 x 10

-6

= =

(8x 10-2) 3 / 2 162 x 10-3

= 0.555 x 10-3

B = 5.55 x 10-4 T

19. A rectangular coil of 500 turns and area 6 x 10-4 m2 is suspended inside a radialmagnetic field of induction 10-4T by a suspension wire of torsional constant5 x 10-10 Nm/degree. Calculate the current required to produce a deflection of 100

[June 2006, Oct -09, March -13, Sep - 15]

N = 500; A=6 x 10

-4

;B=10

-4

TC = 5 x 10-10 Nm / degree = 10, I=?I = C / NBA

5 x 10-10x10 10-3 = =

5 x 102x6 x 10-4x10-4 6I = 0.166 mA

20. A moving coil galvanometer of resistance 20 Ω produces full scale deflection fora current of 50mA. How you will convert the galvanometer into (i) an ammeter of range20A and (ii) a voltmeter of range 120V.

[March : 2007

,March : 2009>

June -13, March -=15]G = 20 Ω ; Ig = 50 mA; (i) 20 A an ammeter range 20 A. I = 20 A = 20000 mA

S = Ig G

I-Ig

a = 4 x 10 -

x = 4 x 10 -


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1

50= 20

20000-50

50

= x 2019950

S = 0.05 Ω / A shunt of 0.05 Ω should be connected in parallel

(ii) 120 v a voltmeter range v=120 R=?

V - GR= Ig

= 120 -2050 X10-3

= (120000 / 50 ) -20

=2380 Ω / A resistance of 2380 Ω should be connected in series with the galvanometer

21. A long straight wire carrying current produces a magnetic induction of 4 x 10-6 Tat a point, 15 cm from the wire. Calculate the current through the wire

[Oct -2007]a=15 x 10-6 m; B=4 x 10-6 T; I=?B=2 x10-7 x I / a

/ I= B x a / 2 x 10-7

=4 x 10-6 x15 x 10-2 / 2 x 10-7 I=3A

22. In a hydrogen atom electron moves in an orbit of radius 0.5 A making 1016 revolutions per second. Determine the magnetic moment associated with orbital motionof the electron. [June- 2008]

radius r= 0.5 x 10-6mn=1016 revolution / Second.

e=1.6 x 10

-19

cl=?l = I x AI=e/T =e.nA=r 2

/l =en x r 2

=1.6 x 10-19 x 1016 x 3.14 x (0.5 x 10-10)2

l =1.256 x 10-23Am-2


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23. Two parallel wires each of length 5cm are placed at a distance of 10cm apart inair. They carry equal currents along the same direction and experience a mutuallyattractive force of 3.6 x 10-4 N Find the current through the conductors.

[Oct 2009; June 2010, March 2013]

a = 10 x 10

-2

m; l=5m; F=3.6 x 10

-4

NI1 = I2 = I =?2 x 10-7 x I1I2

F = x l a

2 x 10-7 x I2 x l F = a

F x a/ I2 =

2 x 10

-7

xl

3.6 x 10-4x10x10-2

=2 x 10-7 x 5

I2 = 36I = 6A

24. A galvanometer has a resistance of 40 Ω It shows full scale deflection for a currentof 2mA. How you will convert the galvanometer into a voltmeter of range o to 20v?

[Oct – 2010]G = 40 Ω; Ig = 2 x 10-3A; V = 20VR=?

VR = -G

Ig

20= - 40

2 x 10-3

20000= 2 -40

= 10000-40R = 9960 Ω/ A resistance of 9960 Ω should be connected in series


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25. Two straight infinitely long parallel wires carrying equal currents and placed at adistance of 20cm apart in air experience a mutually attractive force of 4.9 x 10-5 N perunit length of wire, calculate the current [Oct-2011]

F = 4.9 x 10-5 N; a=20 x 10-2 m; l=1mI1 = I2= I=?

F = 2 x 10

-7

x I1I2 xl

aF = 2 x 10-7 x I2 x l

aF x a

l2 = 2 x 10-7x l 4.9 x 10-5x20 x 10-2

=2 x 10-7x 1

l2 = 49I = 7A

26. The deflection in a galvanometer falls from 50 divisions to 10 divisions when12 Ω resistance is connected across the galvanometer. Calculate the galvanometerresistance

[Sep 2012] S=12 Ω; =50 divisions

g =10 divisions G=? G = s I α

-g/G= s

g

50 – 10= x 12

10

40= x 12

10G = 48 Ω

27. A Current of 4A flows through 5 turn coil of a trangent galvanometer having a

diameter of 30cm. if the horizontal component of Earth’s Magnetic induction is

4x10-5

T, find the deflection produced [March – 14]

2a = 30x10-2 m; n=5; I = 4A;Bh = 4x10-5 T; =?

I = x tan


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tan =

=

= =

tan = 2.093

= 2.093

= 64o28’

28.

A rectangular coil of area 20cm X 10 cm with turns of wire is suspended in

a radial magnetic field of induction 5x10-3T If the galvanometer shows an

angular deflection of 15o for a current of 1mA. Find the torisional constant

of the suspension wire. [June - 14]

A = 20 cm X 10 cm = 20x10x10-4 m

B = 5x10-3 T

I = 1mA

C = ?I =

C =

=

= 0.66x10-6

C = 6.6x10-7 Nm/degree(Or) 381.7x10-7 = 3.81x10-5 Nm/radian


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29. In an Tangent galvanometer, a current of 1A produces a deflection of 30o, Find thecurrent required to produce a deflection of 60o. [Sep – 14]

I1 = 1A; 1 = 30o

I2= ?; 2 = 60o

I

=

I2 =

I2 =

I2 =

I2 = 3A

30. A Uniform magnetic field of induction 0.5T acts perpendicular to the plane of the

dees of a cyctotorn. Calculate this frequency of the oscillator to accelerate protons m p

=1.67x10-27 kg) (Sep – 15)

B = 0.5 T; m p = 1.67x10-27 kg q = 1.6 x 10-19 c

Frequency = ?

31. An A.C generator consists of a coil 10,000 turns and of area 100cm2 The coilrotates at an angular speed of 140 rpm in a uniform magnetic field of 3.6 x 10-2 T.Find the maximum value of the emf induced. [June 2009]

N =104 turns; A=100 x 10-4 m2

B = 3.6 x 10-2 T;E0 =

? =140 rpmE0 = N A B = N A B 2π γ =140 / 60 rpsE0 =10

4 x100 x10-4 x3.6 x 10-2 x2 x3.14x140/60E0 = 52.752 V


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32 .A Soap film of retractive index 1.33, is illuminated by white light incident at anangle 300. The reflected light is examined by spectroscope in which dark bandcorresponding to the wave length 6000 Å is found. Calculate the smallest thicknessof the film. [Oct-2007, Sep -2013]

µ=1.33; i=30; n=1 (smallest thickness)

=6000 Å, t=?If dark band 2 µt cosr = n t=n / 2 µcos r

µ=sin i / sin r

sin i sin30 sinr = = =0.373 r = sin -1 0.3759

µ 1.33 r = 2204

1 x 6000 x 10-10

t =2 x 1.33 x cos 2204

6000 x 10-10

t =2 x 1.34 x 0.9267

t= 2.434 x 10-7 m

33. In young’s experiment of a light of frequency 6 X 1014 Hz is used distance between the centres of adjacent fringes is 0.75 mm. Calculate this distance between the slits, if the screen is 1.5m away.

[Oct-2007 – Sep 14, June - 15] = 6 X 1014 HZ; = 0.75 X 10

-3m D = 1.5 m d = ? = D /d [ = c / ] = C D / .d

/ d = C D / . 3 x 1 08 x1. 5

=

6 x1014 x0.75 x 10-3d = 1 x 10-3 = 1m m


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34. A parallel beam of monochromatric light is allowed to incident normally on a plane transmission grating having 5000 lines per centimetre. A second order spectral lineis found to be diffracted at an angle 300 Find the wave length of the light.

[March 2008, March 2010, June -12] N = 5000 lines / cm

= 5 x 10

5

lines / mm = 2 = 30 = ?

sin = Nm = sin / Nm

= sin 30 / (5 x105 x 2)= 1= 2x5x105x2= 0.5 x 10-6

= 5000 x 10-10 m

= 5000 A

35. A monochromatic light of wavelength 5893 A is incident on a water surfacehaving refractive index 1.33 Find the velocity frequency and wavelength of light inwater . [Oct – 2008, March -11]

= 4 / 3 = 5893 A Velocity of Cw = ? w = ? = ?

Cw = C / 3 x 108

=

4 /39

Cw = x 108

4= 2.25 x 108 ms-1

w = / 5893 x 10-10

=

4 /35893 x 10-10 x 3

=

4= 4419.75 x 10-10m

= C /

3 x 108= [ frequency in water = frequency in air]

5893 x 10-10

= 5.09 x 1014 HZ


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36.In a Newton’s rings experiment the diameter of the 20th dark ring was found to be 5.82mm and that of the 10th ring 3.36mm. If the radius of the plano convex lens is 1 m.Calculate the wavelength of light used.

[March : 2010, March – 14, Sep - 15]

d20 = 5.82 x 10

-3

m ; d10 = 3.36 x 10

-3

mn + m = 20; n = 10; m = 10 ; R = 1 m = ?

d2n+m - d2n d

220 - d

210

= =4mR 4mR

(5.82 x 10-3)2 - (3.36 x 10-3)2

=

4 x 10 x 1

(5.82 +3.36) (5.82-3.36 )x 10-6

=

40 = 9.18 x 2.46 x 10-6 /40 = 0.56457 x 10-6 = 5.645 x 10-10 m = 5645 A

37. A plano – convex lens of radius 3m is placed on an optically flat glass plate and isilluminated by monochromatic light. The radius of the 8th dark ring is 3.6mm. Calculate

the wave length of light used. [March : 2011]R= 3 m; r 8=3.6 x 10

-3m ; n=8; = ? = r 2n / nR

3.6 x 3.6 x 10-6 =

8 x 3= 0.54 x 10-6 =5400 x 10-10 m

= 5400 A

38. A Plane transmission grating has 5000 lines / cm. Calculate the angular separation insecond order spectrum of red line 7070Å and blue line 5000Å [June -2013, June - 15]

N = 5000 lines / cm (or) N = 5x105 lines per meterm = 2> λR = 7070 Å; λV = 5000 Å

R – v = ?Sin = Nm λ Sin R = 5x10

5 x 2x7070x10-10


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Sin R = 0.707 =

R =450

Sin v = 5x105x2x5000x10-10

Sin v = 0.5 =

v = 30 ºR – v = 45 º -30 º

R – v = 150

39. A 300 mm long tube containing 60 cc of sugar solution produces a rotation of 9o when placed in a polarimeter. If the specific rotation is 60o, calculate the quantity ofsugar contained in the solution

l =300 mm = 3dm [June -2013] v=60 CC, = 9º, S=60º, m =?

s = =

s =

m = = = 3g

40. In a Young’s double slit experiment two concurrent sources of intensity ratio

of 64:1 produce interference f rings. Calculate the ratio of maximum and

minimum intensities. [Sep - 14]

if = 64:1

I a2

/ =

= = =

a1= 8a2


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=

= =

= 81: 49

41. In Newton’s ring experiment the diameter of certain order of dark ring ismeasured to be double that of second ring, what is the order of the ring?

[June - 14] dn = 2d2

n = ?

=

=

=

n = 8

42. Wave length of Balmer second line is 4861 A. Calculate the wave length of firstline. [March : 2007]

2= 4861 A 1 = ?

For Balmer II Line n1 =2; n2 =4

2 = R ( 1 _ 1n1

2 - n22)

1/ 2 = R ( 1 1)22 - 42

= 4 – 1 R16

1/ 2 = 3R / 16

For Balmer I line n1 =2; n2 = 3

1


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2

2 = R 1 _ 1 =22 - 32

= 9 – 4R

36

1/ 1 = 5 / 36 R

1/ 2 =

1/ 2 =27 /20 1 =

1=

1= 6562 A

43. In Bragg’s Spectrometer the glancing angle for first order spectrum was observedto be 8º. Calculate the wave length of x-ray. If d =2.82 x 10-10m. At what angle will thesecond maximum occur?

[June - 2007]1 = 8 ; d= 2.82 x 10

-10m; n=1 = ?

2d sin = n 2d sin

=n

2 x 2.82 x10-10 x sin 8 =

1= 2 x 2.82 x10-10 x0.139

= 0.7849 x 10-10 mn = 2 when 2 = ?

2d sin 2 = n sin 2 = n / 2d

2 x 0.7849 x10-10

=2 x 2.82 x10-10

sin 2 = 0.27832 = sin

-1 0.27832 = 16 9

2

1 2


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44. An - particle is projected with an energy on 4 MeV directly towards a goldnucleus, Calculate this distance of its closest approach (Given atomic number ofgold 79 and atomic number of a α particle =2) [March : 2008]

(Atomic number of Gold = 79, Atomic number of α particle = 2)K.E = 4 x 10-6 x 1.6 x 10-19 J Z=79 r 0 =?

18 x 109

x Ze2

r 0 =

K.E

18 x 109 x 79 x 1.6 x 10-19x1.6 x 10-19

=

4 x 106 x 1.6 x 10-19

= 568.8 x 10-16

r 0 = 5.688 x 10-14 m

45. An electron beam passes through a transverse magnetic field of 2 x 10-3 T and an electric field E of 3.4 x 104 V / m, acting simultaneously. If the path of the

electrons remain undeviated calculate the speed of electrons. If the electric field isremoved what will be the radius of the electron path..? [Oct-2011]E = 3.4 x 104 v / m ; B = 2 x 10-3 Tv = ? r = ?

v = E / B

3.4 x 104 =

2 x 10-3

v = 1.7 10

+7

ms

-1

Bev = mv2 / rBe = mv / r / r = mv / Be

9.11 x 10-31 x 1.7 x107 =

2 x 10-3x1.6 x 10-19

r = 4.839 x 10-2 m46. How fast would a rocket have to go relative to an observer for its length to becorrected to 99% of its length at rest [Oct -2007, Oct -11, March -12, Jun - 14]

99when l = lo ; ν = ?

100

l = lo 1-v2 / c2

99lo= lo 1-v

2 / c2 1000.99 = 1-v2 / c2

(0.99)2 = 1-(v2 / c2)


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(c2-v2) / c2 = 0.992

c2-v2 = (0.99c)2

v2 = c2 -0.9801 c2

= c2 (1-0.9801)

v2 = 0.0199 c2

v = 0.141 c

= 0.141 x 3 x 108

v = 0.423 x 108 ms-1

47. At what speed is a particle moving if the mass is equal to three times its restmass? [Oct-2008, Sep – 14, June - 15]

m = 3 m0v = ?

m0m =

1 -v2 / c2

m0

3 m0 = 1 -v2 / c2 3 1 -v2 / c2 = 1

9(1 -v2 / c2) = 1

9 (c2-v2) /c2 = 1

9c2 - 9v2 = c2

9v2 = 9c2 - c2

9v2 = 8c2

v2 = 8 c2 / 9

v = 22 c / 3= 22 x 3 x 108 / 3

v = 22 x108 ms-1

v =2.828 ms-1

48. The time interval measured by an observer at rest is 2.5 x 10-8 s What is the timeinterval as measured by an observer moving with velocity v=0.73c [June - 2009]

to = 2.5 x 10-8 s

v = 0.73c t = ?t = to / 1 -v

2 / c2

v2 / c2 = 0.5329 c2 / c2

1 – (v2 / c2 )= 1 - 0.5329 = 0.4671

1 -v2 / c2 = 0.4671 = 0.6834

t = t0 / 0.6834

= 2.5 x 10-8 / 0.6834 = 3.658 x 10-8 s


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49. Work function of Iron is 4.7eV Calculate the cut off frequency and the correspondingcut off wavelength for this metal

[June 09, March 2012]w = 4.7 e V

w = 4.7 x 1.6 x 10-19

Jo = ? o =?w = h oo = w / h

4.7 x 1.6 x 10-19

=6.626 x 10-34

o = 1.134 x 1015

o = c / o

3x 108

=

1.134 x 1015

= 2.645 x 10-7

o = 2645 A 50. A metallic surface when illuminated with light of wavelength 3333 A emits electronswith energies up to 0.6ev. Calculate the work function of the metal

[Oct 2009, June 2012, March 2013] = 3333A K.E = 0.6 e v w = ?h = w + k.E

w = h -k.E

w = h.c / - k.E6.626 x 10-34 x 3 x 108 = - 0.6

3333 x 10-10 x 1.6x 10-19

w = 3.727 – 0.6w = 3.127 eV

51. A proton is moving at a speed of 0.900 times the velocity of light Find the kineticenergy in joules and Mev. [March: 2011]

v = 0.9 c; mo = 1.67 x 10-27 kg

(m- mo)c2 = ?

m = mo/ 1 -v2 / c2

1.67 x 10-27 =

1- 0.81 c2 / c2

1.67 x 10-27 1.67 x 10-27 = =

1- 0.81 0.19


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mo = 3.831 x 10-27 kg

m - mo = (3.831 x 10-27-1.67 x 10-27)

= 2.161 x 10-27

(m - mo) c2 = 2.161 x 10

-27 x 9 x 1016 (m - mo) c

2 = 19.449 x10

-11 J

19.449 x 10

-11

E =1.6 x 10-19

= 12.155 x10-11 x 10-19ev= 12.155 x108

E = 1215 Mev

52. What is the de Braglie wave length of an electron of Kinetic energy 120ev?[Oct-2012]

If. k.E = 120 evv = 120 v = ?

= (12.27 / v) Å= (12.27 / 120)= (12.27 / 10.95)

= 1.121 A 53.The rest mass of an electron 9.1x10-31 Kg What will be it’s mass if it moves

with 4/5th of the speed of light [June - 14]

m = 9.1x10-31

=m = ?

m =

=

=

=

=

=


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=m = 15.16x10-31 Kg.

54. Calculate the Debroglie wavelength of an electorn if the speed 105 ms-1 (given m = 9.1x10-31 kg; h = 6.626x10-34 JS) (Sep – 15)

m = 9.1x10-31 Kg

h = 6.626x10-34 Js

ms-1

=

= 0.7281x10-8

72.81 AO

55. A piece of bone from an archaeological site is found to give a count rate of 15counts per minutes A similar sample of fresh bone gives a count rate of 19 counts perminute. Calculate the age of the specimen (Given T1/2= 5570 Years)

[Oct - 2011, March- 2006> Sep -2013, March – 2014] N = 15 counts / minute T1/2=0.693 / N0 = 19 counts minutet = ? N = N0 e

- t

N / N0 = e- t

N0 / N = e t

l oge(N0 / N) = t

t= loge = x2.303x loge

t= x 2.303 x log 1.266

5570t = x 2.303 x .1026

0.693t = 1899 Years

56. Calculate the energy released when 1Kg of 92U235 undergoes nuclear fission.

Assume, energy fission is 200 Mev. Avagadro Number =6.023 x 1023 Express youranswer in Kilowatt hour also [March : 2006, Sep -2011, Sep 2013]

Energy produced fission = 200 Mev = 200 x106 x1.6 x10-19 J = 3.2 x 10-11

Avagadro Number N = 6.023 x 1023


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1 kg 92U235 Energy released f 1kg 92U

235 = ? 235 g 92U

235 Number of atoms in 235 g of uranium = 6.023 x 1023

Number of atoms in 1Kg (or ) 1000 g of uranium 92U235 –

= 6.023 x 1023 x 1000

235

= 2.562 x 1024

Energy produced by 1 kg of uranium during fission = 2.562 x 1024 x 3.2 x 10-11

E = 8.2016 x1013J1 k w h = 3.6 x 106J

8.2016 x1013 E = = 2.2782 x 107 k w h

3.6 x 106

57. Find the energy released when two 1H2 nuclei fuse together to form a single 2He

4

nucleus. Given the binding energy per nucleon of 1H2 a single 2He

4 nucleus, Given the

binding energy per nucleon of 1H

2

and 2He

4

are 1.1 Mev and 7.0 Mev respectively,[June 2006, October 2012]

1H2-BE/A of = 1.1 Mev

2He4- BE/A of = 7 Mev21H

2

2He4 + Q

Energy released Q = ?BE/A of 1H

2- = 1.1 Mev

BE of 1H2- = 2 x 1.1 Mev = 2.2 Mev

BE/A of 2He4 = 7 Mev

BE of 2He4 = 4 x 7=28 Mev

21H2

2He4 + Q

2 x 2.2 28 + Q4.4 28 + Q/Q = 28 – 4.4 = 23.6 Mev

58. A reactor is developing energy at the rate of 32 MW. Calculate the requirednumber of fissions per second of 92U

235 Assume that energy per fission is 200 Mev.

[June - 2006,2008,2011, March – 14]Energy / fission = 200 MeV = 200 x 106 x 1.6 x 10-19

Total Energy = 32 MW

No of fission of 92U23

=32 x 106

N =

200 x 106 x 1.6 x 10-19

N = 1018 fission / Second


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59. Show that the mass of radium (88Ra226) with an activity of 1 curie is almost a

gram [June - 2006,March :2008, March :2012]

[T ½ - 1600 Years ; 1 curie = 3.7 x1010 disintegration / second]

T½ =1600 Years=1600 x 365.25 x 24 x 60 x 60

dN / d t = 3.7 x 1010 disintegration / Second m = ? T ½ = 0.6931 /

dN / d t = N N = 1 dN

d t

T ½ dN= x

0.6931 dt

1600 x 365.25 x 24 x 60 x60 N = X 3.7 x 1010

0.6931= 2.695 x 1021

According to Avagadro’s Principle, 6.023 x 1023 atoms = 226 g ofRadium, 2.695 x 1021 atoms

226m = x 2.695 x 1021

6.023 x 1023

= 1.011 gm 1g

60.Calculate the mass of coal required to produce the same energy as that produced by thefission of 1 Kg of 92U

235 [October -2006]

Energy fission = 200 Mev = 200 x 1.6 x 10-19 x 106

Avagadro Number =6.023 x 1023

Heat of combustion of Coal = 33.6 x 106 J / kg-

Mass of Coal= ? Number of Atoms in 235 g U 235 – = 6.023 x 1023 Number of Atoms in 1000 g ( or ) 1 kg U 235

6.023 x 1023

N= x 103 = 2.562 x 1024

2351 Energy/fission =3.6 x1011 JEnergy produced by the fission of 1Kg of U235 ; = 2.562 x 1024 x3.6 x10-11


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E = 8.2016 x 1013JLet M be the mass of the coal required to produced equivalent to energy produced by1Kg of U 235

M x Heat of combustion of Coal =8.2016x 1013

M x 33.6 x 10

6

= 8.2016 x 10

13

8.2016 x 1013

M = = 2.441 x 106 kg = 2441x103 Kg33.6 x 106

M = 2441 ton.61. Mass defect of 6C

12 is 0.098 amu. Calculate the B.E /A of 6C12 nucleus.[June - 2007]

m of -6C12 = 0.098 amu; A=12

BE / A = ? m of -6C

12 = 0.098 amu

BE of -6C12

= m x 931 Mev= 0.098 x 931 MeV= 91.238 MeV

BE/A Of - 6C12 = 91.238 /12 = 7.603MeV

62. Calculate the time required for 60% of a sample of radon to undergo decay.Given T1/2 redon =3.8 days [March : 2007]

Half life of Rn ; = 3.8 days Original Amount N0 = 100% ; Amount of Sample disintegrated ( N0 – N )= 60%Amount of Sample present N = 40% time required t=?

T1/2 = 0.6931

0.6931 =

T1/2 N = N0 e

- t

N / N0 = e t

N0/ N = e t

log (N0/ N) = t

t = loge = x2.303x loge

t= x 2.303 x log 2.5 3.8

t = 2.303 x log 10 2.5

0.69313.8

t = 2.303 x 0.39790.6931

t = 5.022 days


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63. The binding energy per nucleon for 6C12 nucleus is 7.68 MeV and that for 6C

13 is7.47 MeV. Calculate the energy required to remove a neutron from 6C

13 nucleus[March: 2009> March - 15]

BE/A of - 6C12 = 7.68 Mev

BE/A of - 6C13 = 7.47 Mev

BE/A of Q = ?6C

13

6C12 +0n

1 +Q.BE/A of - 6C

13 = 7.47 Mev

Total BE of C13= 13 x 7.47 MeV= 97.11 MeV

6C12- BE/A = 7.68 Mev

Total BE of 6 C12

= 12 x 7.68 Mev= 92.16 Mev

Binding Energy of a neutron = = BE of 6C13 --BE of 6C

12

= 97.11 – 92.16 = 4.95 MeV

64.. Calculate the energy released in the following reaction

3Li6 +0n

1 2He4+1H

3

Given Mass of 3Li6 – = 6.015126 amu

Mass of 0n1= 1.008665 amu

Mass of 2He4 = 4.002604 amu

Mass of 1H3 = 3.016049 amu

/ Mass of the reactants ; =?Mass of 3Li

6 = 6.015126 amu Mass of 0n

1= 1.008665 amu +

7.023791 amu

Mass of 2He4 = 4.002604 amu

Mass of 1H3 – = 3.016049 amu

7.018653

Mass Defect m = Mass of the reactants - Mass of the productsm = 7.023791 - 7.018653m = 0.005138 amu

Energy released in the reaction = m x 931 MeV= 0.005138 x 931 MeV

E= 4.783 MeV


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65. Calculate the energy released in the reaction 13AI27 +1H

2 12Mg25+2He

4

Mass of 13AI27 – = 26.981535 amu

Mass of 1H2 = 2.014102 amu

Mass of 12Mg25 = 24.98584amu

Mass of 2He4= 4.002604 amu

Energy related in the reaction = ?

Mass of reactants 13AI27 – + 1H

2 = 26.981535 +2.014102

= 28.995637 amu

Mass of products 12Mg25 + 2He

4 – = 24.98584 + 4.002604

= 28.988444 amu

Mass of defect = Mass of reactions - Mass of Products

m = 0.007193

Energy released in the reaction E = m x 931 MeV

= 0.007193 X 931 MeV

E = 6.696 Mev

66. A transistor is connected in CE configuration. The voltage drop across the loadresistance (Rc) 3 k is 6V. Find the basic current. The current gain of the transistoris 0.97 [June - 2010]

= 0.97 Rc = 3K VCE= 6V IB =?

Ic = VCE / Rc

= 6 / 3 x 103

= 2x 10-3 A

= / (1 - )

= 0.97 / (1 - 0.97)= 0.97 /0.03

= 32.33

= Ic / IB

IB = Ic /

= 2 x 10-3 / 32.33

= 0.0618 x 10-3

IB = 61.8 x 10-6AIB = 61.8 A


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