SOME TYPICAL SOLVED EXAMPLES

Example 1. Find the binding energy per nucleon for ₃Li⁷ if mass of ₃Li⁷ is 7·01653 amu

[Given : m_p = 1·00759 amu, m_n = 1·00898 amu]

Solution :

Example 2. If the mass defect in the formation of helium from hydrogen is 0·5%, then find the energy obtained in kWh, in forming helium from 1 kg of hydrogen.

Solution :

Example 3. The mass of helium nucleus is less than that of its constituent particles by 0·03 amu. Find the binding energy per nucleon of ₂He⁴ nucleus.

Solution :

Example 4. How much energy is released in the following reaction ?

1H² + ₁H² = ₂He⁴

Given the binding energy per nucleon of ₁H² and

2He⁴ is 1·125 MeV and 7·2 MeV respectively.

Solution :

Example 5. If 200 MeV energy is released in the fission of a single nucleus of ₉₂U²³⁵, how many fission must occur per second to produce a power of 1 kW ?

Solution :

Example 6. The energy supplied to a city by state electricity board is 40 million kilowatt-hour. If this energy could be obtained by the conversion of matter, how much mass would have to be annihilated ?

Solution :

OBJECTIVE QUESTIONS

1. m, m_n and m_p are the masses of

ZX^A nucleus, neutron and proton respectively. If the nucleus is broken into its constituents, then—

(A) m > [(A – Z)m_n + Zm_p] (B) m < [(A – Z)m_n + Zm_p] (C) m = [(A – Z)m_n + Zm_p] (D) m = [Zm_n + (A – Z)m_p]

2. An element A is converted to C through following reactions :

A ⎯→ B + 2He⁴ B ⎯→ C + 2e^– Then—

(A) A and C are isobars (B) A and C are isotopes (C) A and B are isobars (D) A and B are isotopes

3. The nucleus with maximum bind-ing energy per nucleon out of the following is—

(A) ₉₂U²³⁸ (B) ₂He⁴ (C) ₈O¹⁶ (D) ₂₆Fe⁵⁶ 4. The following nuclear reaction

represents

7N¹⁴ + ₁H¹⎯→ ₈O¹⁵ + 7·3 MeV (A) Nuclear fusion

(B) Nuclear fission

nuc-leon of deuterium and helium are 1·1 MeV and 7 MeV respectively.

When two deuterons fuse to form a helium nucleus, the amount of energy released will be—

(A) 23·6 MeV (B) 7 MeV (C) 6 MeV (D) 200 MeV 6. The most suitable material for

moderator in a nuclear reactor is—

(A) D₂O (B) Cd (C) B (D) ₉₂U²³⁵ 7. The energy of thermal neutrons

is nearly—

(A) 0·25 MeV (B) 0·025 MeV (C) 200 MeV (D) 0·025 joule 8. The first atomic reactor was

made by—

(A) Hahn (B) Strassma (C) Fermi (D) Bethe 9. The fissionable material used in

the bomb dropped at the city of Nagasaki of Japan was—

(A) Plutonium (B) Uranium (C) Thorium (D) Neptunium 10. When the number of nucleons in

the nucleus increases, the bind-ing energy per nucleon—

(A) Decreases continuously with A

(B) Increases continuously with A

then decreases

11. The source of solar energy is—

(A) Fission of helium (B) Chemical reaction (C) Burning of carbon (D) Fusion of hydrogen nuclei 12. Average binding energy of

nuc-leons is—

(A) 8 eV (B) 8 MeV (C) 8 BeV (D) 8 joule 13. The energy equivalent to 1 kg of

matter is about—

(A) 10¹¹ joule (B) 10¹⁴ joule (C) 10¹⁷ joule (D) 10²⁰ joule 14. The controller rods in the nuclear

reactor are made of—

(A) Cadmium (B) Uranium (C) Graphite (D) Plutonium 15. Which of the following is the

main source of energy emission in the stars ?

(A) Chemical reaction (B) Fusion of heavy nuclei (C) Fission of heavy nuclei (D) Fusion of lighter nuclei 16. In a nuclear reactor—

(A) Moderator is used to control the number of neutrons (B) Moderator is used to slow

down the speed of neutrons

(D) Coolant is used to control the number of neutrons 17. The equation

4(₁H¹) ⎯→ 2He⁴ + 2e^– + 26 MeV represents—

(A) β-decay (B) γ-decay (C) Fusion (D) Fission 18. The mass defect in a nuclear

fusion reaction is 0·3 per cent.

What amount of energy will be liberated in one kg fusion reac-tion ?

(A) 5·2 × 10¹⁴ joule (B) 2·7 × 10¹⁴ joule (C) 2·7 × 10¹⁴ kWh (D) None of these

19. Enriched uranium is better fuel for a reactor because it has grea-ter proportion of—

(A) Slow neutrons (B) Fast neutrons (C) ₉₂U²³⁵ (D) ₉₂U²³⁸

20. In a nuclear reactor—

(A) Rate of reaction may be controlled by boron steel rods

(B) Fast neutrons are slowed down by cadmium rods (C) Plutonium is used as coolant (D) Hydrogen is used as fuel

ANSWERS WITH HINTS

●●●

UPKAR PRAKASHAN, AGRA-2 E-mail : [email protected]

By : Dr. Lal, Mishra & Kumar Code No. 1624 Rs.

250/-Useful for Various Competitive Exams.

Website : www.upkar.in

1. Which of the following is India’s first geostationary satellite ? (A) Apple

(B) INSAT-B (C) Aryabhatta (D) Rohini

2. A body is rolling down an inclined plane. Its translational and rota-tional kinetic energies are equal.

The body is a—

(A) Solid sphere (B) Hollow sphere (C) Solid cylinder (D) Hollow cylinder

3. Which of the following is the main source of electricity in our country ?

(A) Nuclear energy (B) Hydro electricity (C) Thermal energy (D) Geothermal energy

4. A combination of two thin convex lenses of focal length 0·3 m and 0·1 m will have minimum sphe-rical and chromatic aberrations if the distance between them is—

(A) 0·1 m (B) 0·2 m (C) 0·3 m (D) 0·4 m 5. A free-floating astronaut ‘P’

pushes another free-floating astronaut ‘Q’ in space. The mass of P is greater than that of Q.

The force exerted by astronaut P on astronaut Q will be—

(A) Equal to zero

(B) Equal to force exerted by Q on P

(D) Less than the force exerted by Q on P.

6. When ₉₂U²³⁵ is bombarded with one neutron, fission occurs and the products are three neutron,

36Kr⁹⁴, and—

(A) ₅₆Ba¹⁴¹ (B) ₅₄Xe¹³⁹ (C) ₅₆Ba¹³⁹ (D) ₅₃I¹⁴²

7. Scratch pad memory is used to—

(A) Support main programme (B) Store small amounts of

infor-mation that can be fetched when needed

8. In Bohr’s model of hydrogen atom, which of the following pairs of quantities are quantized ? (A) Energy and linear

momen-tum

(B) Linear and angular momen-tum

(D) None of the above

9. The activity of a sample of a radioactive material is A₁ at time t₁ and A₂ at time t₂; (t₂> t1). Its mean life is T. Then—

(A) A₁t₁ = A₂t₂ (B) A₁ – A₂

t₂ – t₁ = Constant (C) A₂ = A₁ e⁽^{t1 – t2)/T} (D) A₂ = A₁ e

t1 t2 T

10. TheoutputofaNAND gate is 0—

(A) If both inputs are 0

(B) If one input is 0 and the other input is 1

(D) Either if both inputs are 1 or if one of the inputs is 1 and the other 0

11. The maximum frequency ν of continuous X-ray is related to the applied potential difference V as—

(A) ν ∝ V (B) ν ∝ V (C) ν ∝ V^3/2 (D) ν ∝ V² 12. An electron, a proton, a deuteron

and an alpha particle, each having the same speed are in a region of constant magnetic field perpendicular to the direction of thevelocitiesof the particles. The

radius of the circular orbits of these particles are respectively R_e,R_p,R_dandR_α.Itfollowthat—

(A) R_e = R_p (B) R_p = R_d (C) R_d = R_α (D) R_p = R_α 13. A body of mass m slides down a

rough plane of inclination α. If μ be the coefficient of friction, the acceleration of the body will be—

(A) g sin α (B) g μ cos α

14. Spherical aberration in a lens—

(A) Is minimum when most of the deviation is at the first surface

(B) Is minimum when most of thedeviationisatthesecond surface

above considerations 15. In the given arrangement of

springs, the time-period of verti-cal oscillations of the mass m is—

(A) T = 2π m k₁ + k₂ (B) T = 2π k₁ + k₂

k₁ + k₂

16. Kepler’s second law (law of areas) is nothing but a statement of—

(A) Work-energy theorem (B) Conservation of linear

mo-mentum

(D) Conservation of energy

17. The kinetic energy E_k of a photoelectron varies with the frequency ν of the incident radia-tion as which of the following graph ?

18. The equation of a travelling wave is given by

y = 0·5 sin (20x – 400 t) where x and y are in metre and t is in second. The velocity of the wave is—

(A) 10 m/s (B) 20 m/s (C) 200 m/s (D) 400 m/s 19. APT is used—

(A) In inventory management (B) In CAM for NC machine

tools

20. The radiation energy density per unit wavelength at a temperature T has a maximum at a wave-length λ0. At temperature 2T, it will have a maximum at a wave-length—

(A) 4λ0 (B) 2λ0

21. A magnetising field of 1600 Am^–1 produces a magnetic flux of 2·4 × 10^–5 Wb in an iron bar of cross-section area 0·2 m². The succeptibility of bar is—

(A) 596 (B) 1192 (C) 298 (D) 1788 22. A short bar magnet, placed with

its axis at 30° with an external magnetic field of 0·16 T, expe-riences a torque of magnitude 0·032 J. The magnetic moment of the bar magnet is (in units of J/T)—

(A) 4 (B) 2

23. An iron tore supports N turns. If a current i produces a magnetic flux across the tore’s

cross-section equal to φ, then the magnetic field energy is—

(A) N i φ (B) 1 2 N φ i (C) N² i φ (D) N i²φ 24. A circular metal plate of radius R

is rotating with a uniform angular velocity ω with its plane perpen-dicular to a uniform magnetic fieldB.Thenthee.m.f.developed between the centre and the rim of the plate is—

(A) πω^BR² ^(B) ω^BR² (C) πω^BR²^/2 ^(D) ω^BR²^/2 25. The magnetic field inside a

toroidal solenoid of radius R is B.

If the current through it is doubled and the radius is also doubled keeping the number of turns per unit length the same, the magnetic field produced by it will be—

(A) 4 B (B) 2 B (C) B

2 (D) B

26. A water tank, open to the atmos-phere, has a leak in it in the form of a circular hole, located at a height h below the open surface of water. The velocity of the water coming out of the hole is—

(A) gh/2 (B) gh (C) 2gh (D) 2 gh 27. The amplitude of an oscillating

simple pendulum is 10 cm and its period is 4 sec. Its speed 1 second after it passes its equili-brium position is—

(A) Zero (B) 0·157 m/s (C) 0·212 m/s (D) 0·32 m/s 28. A wave is represented by the

equation y = a cos (kx + ω^{t) is} superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation of the other wave is—

(A) a sin (kx + ω^t⁾ (B) –a sin (kx – ω^t⁾ (C) –a cos (kx + ω^t⁾ (D) – a cos (kx – ω^t⁾

29. A person sitting in a rotating merry-go-round will feel—

(A) An inward force (B) An outward force

(D) An inward or outward force depending upon his weight and the velocity of rotation of the merry-go-round

30. InYoung’sdoubleslitexperiment, the separation between the slits is halved and the distance bet-ween the slits and screen is doubled. The fringe-width will—

(A) Be halved (B) Be doubled (C) Be quadrupled (D) Remain unchanged

31. A temperature of 4K on the Fahrenheit scale will be nearly—

(A) 36° F (B) 39°F (C) – 237°F (D) – 452°F 32. A square of side ‘a’ has charge Q

at its centre and charge ‘q’ at one of the corners. The work required to be done in moving the charge

‘q’ from the corner to the diago-nally opposite corner is—

(A) Zero (B) Qq 4πε0a (C) Qq 2

4πε0 a (D) Qq 2πε0 a 33. If the rms speed of the

mole-cules of a gas at 27°C is 141·4 m/s, the rms speed at 327°C will be nearly—

(A) 1697 m/s (B) 565·6 m/s (C) 282·8 m/s (D) 200 m/s 34. The magnetic susceptibility of

any paramagnetic material chan-ges with absolute temperature T as—

(A) Directly proportional to T (B) Remains constant (C) Inversely proportional to T (D) ExponentiallydecayingwithT 35. Hot incandescent liquids and solids produce a…… spectrum.

(A) Line (B) Band (C) Continuous (D) None of the above

36. An electric dipole of moment → p placed in a uniform electric field

→E has minimum potential energy

when the angle between → p and

→E is—

(A) Zero (B) π 2

37. The intensity of different order maxima is nearly the same in—

(A) Young’s double slit experi-ment

(B) Single slit diffraction pattern (C) Double slit diffraction pattern (D) All the above

38. X-rays are produced by accelera-ting electrons by voltage V and letting them strike a metal of atomic number Z. The highest frequency of X-rays produced is proportional to—

(A) V (B) Z

a beam of—

(A) Electrons (B) Protons (C) Neutrons

(D) Positively charged ions 40. 70 calories of heat is required to

raise the temperature of 2 moles of an ideal gas from 30°^{C to} 35°C while the pressure of the gas is kept constant. The amount of heat required to raise the temperature of the same gas through the same temperature

range at constant volume is (Gas constant R = 2 cal/mol-K)—

(A) 70 calories (B) 60 calories (C) 50 calories (D) 30 calories 41. The amount of U²³⁵ in a sample

of 20 g of naturally occurring uranium will be nearly—

(A) 10 g (B) 14 g (C) 3·36 g (D) 0·14 g 42. A body is thrown vertically

upwards with a velocity u. The distance travelled by it in the fifth and the sixth seconds are equal.

The velocity u is given by—

(g = 9·8 m/s²) (A) 24·5 m/s (B) 49·0 m/s (C) 73·5 m/s (D) 98·0 m/s 43. The ionic crystals are not

usually—

(A) Poor conductors

(B) Opaque to visible radiation (C) Of high melting points (D) Very stable

44. A coil of N = 100 turns carries a current I = 5A and creates a magnetic flux φ^{= 10}^{– 5}^Tm²^per turn. The value of its inductance L will be—

(A) 0·05 mH (B) 0·10 mH (C) 0·15 mH (D) 0·20 mH 45. The amplitude of a particle in

S.H.M. decreases from 20 cm to 15 cm in 2 minutes. Its energy decreases by nearly—

(A) 44% (B) 25%

46. The kinetic energy of an electron with de-Broglie wavelength of 0·3 nanometer is—

(A) 0·168 eV (B) 16·8 eV (C) 1·68 eV (D) 2·5 eV 47. The intensity of sound waves in

a medium is directly proportional to—

(A) Square root of wave speed (B) Square of the density of the

medium

is proportional to (A is the mass number and Z the atomic num-ber)—

(A) A (B) A^1/3 (C) Z (D) Z^1/3

49. The brightness of a bulb will be reduced if a resistance is con-nected in—

(A) Series with it (B) Parallel with it

p is placed in an electric field of strength E. Initially the dipole is aligned parallel to the field. If the dipole is to be rotated to be anti-parallel to the field, the work required to be done by an exter-nal agency is—

(A) –2p E (B) – p E (C) p E (D) 2p E

ANSWERS WITH HINTS

●●●

(Continued from Page 1071) CSV—From what level of educa-tion should an aspirant begin pre-paring for it ?

Dhananjay—After10thstandard.

Personal Qualities

Hobbies—Driving, Basket ball Ideal Person—My father

StrongPoint—Myparents support-ing behaviour

Weak Point—Really I don’t give sufficient time for studies

CSV—What was your order of preference for various branches for which this test is held ?

Dhananjay—Firstly M.B.B.S.

then B.D.S.

CSV—What help do the science magazines render in the preparations for this examination ?

Dhananjay—They give us the latest information and many other necessary facts to crack exams like AIIMS, MGIMS etc.

CSV—What will be your criterion for selecting a magazine for these examination ?

Dhananjay—A good magazine should be precise and full of easy formulae and tricks.

CSV—What isyour opinion about ourCompetitionScienceVision ? How

much helpful and useful do you find it ?

Dhananjay—CSV is a landmark in the field of science magazines. It gives all important facts with easily understandableshort explanations.

CSV—Please suggest in what way CSV can be made more useful for medical aspirants.

Dhananjay—By providing more model papers with Assertion and Reason type questions.

CSV—Please mention your posi-tion in the merit list as well as the marks obtained in different subjects.

Whatwasyouraggregatepercentage of marks ?

Dhananjay—4th rank Physics—35/50 Chemistry—43/50 Zoology—41/50 Botany—41/50 Total—160

CSV—What books/magazines/

newspapers did you read for G. K.

preparations ?

Dhananjay—Newspapers and T.V. News.

CSV—Whom would you like to give the credit for your success ?

Dhananjay—My respected mother and father and my Bhaiya-Bhabhi also helped me a lot and unforgettable support of my teachers and classmates.

CSV—Please tell us something about your family.

Dhananjay—My father is a lecturer in Electronics Engg. Deptt.

M. G. Polytechnic Hathras,my mother is a house-wife. I have only one elder brother who is sales engineer in Delhi and Bhabhi house-wife.

CSV—What in your frank opinion has been the biggest mistake in your preparation for this test ?

Dhananjay—I had no planning in my mind about the career which is very-very important because in medical stream time has very much importance.

CSV—What message would you like to give for our readers of CSV ?

Dhananjay—Belief in God and firm determination and Blessings of your parents and teachers are something which do more than the hardwork.

●●●

1. Two vectors →

A and → B are in-clined to each other at an angle θ. Which of the following is the unit vector perpendicular to both

→A and → 2. The dimension of RC is—

(A) Time (B) Inverse time (C) Square of time (D) Square of inverse time 3. A number of bullets are fired in

all possible directions with the same initial velocity u. The maxi-mum area of ground covered by bullets is—

4. Two particles having mass M and m are moving in a circular path having radius R and r. If their periods are same, the ratio of angular velocity will be—

(A) r

R (B) R

5. Three blocks of masses 2 kg, 3 kg and 5 kg are connected to one another with light strings and are then placed on a smooth

T₁ T₂

2kg 3kg 5kg

1m/sec² F

frictionless horizontal surface.

The system is pulled with a force F from the side of the lightest mass so that it moves with an acceleration of 1 ms^–2 . T₁ and

T₂ denote the tensions in other strings. The value of F is—

(A) 2 N (B) 3 N (C) 5 N (D) 10 N 6. The kinetic energy acquired by a

mass (m) in travelling distance (s) starting from rest under the action of a constant force is directly proportional to—

(A) 1

√⎯

^m ^(B) ^m

(C)

√⎯

^m ^(D) ^m⁰

7. A metal ball of mass 2 kg moving with a velocity of 36 km/h has a head on collision with a statio-nary ball of mass 3 kg. If after the collision, the two balls move together, the loss in kinetic energy due to collision is—

(A) 40 J (B) 60 J (C) 100 J (D) 140 J 8. The escape velocity from the

surface of the earth is v_e. The escape velocity from the surface of a planet whose mass and radius are three times those of the earth, will be—

(A) v_e (B) 3 v_e (C) 9 v_e (D) 1

3 v_e

9. A disc revolves in horizontal plane at a steady rate of 3 rev/s.

A coin just remains on the disc if kept at a distance of 2 cm from the axis of rotation. What is the coefficient of friction between the coin and the disc ?

(A) 0·5 (B) 0·65 (C) 0·7 (D) 0·75

10. A ring of mass m and radius r rotates about an axis passing through the centre and perpendi-cular to its plane with angular velocity ω. Its kinetic energy is—

(A) mrω² (B) mr²ω² (C) 1

2 mrω² (D) 1 2 mr²ω² 11. The dimension of gravitational

field is same as that of—

(A) Force (B) Velocity

12. The translational degree of free-dom of an ant moving in a plane is—

(A) 0 (B) 1

13. In a surface tension experiment with a capillary tube water rises upto 0·1 m. If the same experi-ment is repeated in an artificial satellite, which is revolving around the earth; water will rise in the capillary tube upto a height of—

(A) 0·1 m (B) 0·2 m (C) 0·98 m

(D) Full length of tube

14. A thermodynamic process is shown in the figure. The pres-sures and volumes correspond-ing to some points in the figure are

P_A = 3 × 10⁴ N/m², V_A = 2 × 10^{– 3} m³ P_B = 8 × 10⁴ N/m², V_B = 5 × 10^{– 3} m³

In the process AB, 600 J heat is added to the system and in the process BC, 200 J of heat is added to the system. Thechange in internal energy of the system in process AC would be—

(A) 800 J (B) 600 J (C) 640 J (D) 560 J 15. One poise is—

(A) 1 dyne sec/cm² (B) 1/98·1 kgf sec/m² (C) 10^–1 kg/m-sec (D) Any of the above

16. A particle executes simple har-monic motion with a frequency f.

The frequency with which its kinetic energy oscillates is—

(A) f

2 (B) f

17. We plot the graph having tempe-rature in °C on x-axis and in °F on y-axis. If the graph is straight line, then the correct statement is—

(A) The line intercepts the posi-tive x-axis

(B) The line intercepts the posi-tive y-axis

(D) The line intercepts the nega-tive axis of both x and y axis 18. Two waves having equation

x₁ = a sin (ωt + φ1) and x₂ = a sin (ωt + φ2) superimpose. If in the resultant wave the frequency and ampli-tude remain equal to those of superimposing waves, then phase difference between them is—

19. A 10 kg iron bar (specific heat 0·11 cal/gm °C) at 80°C is placed on a block of ice. How much ice melts ?

(A) 1·1 kg (B) 10 kg (C) 16 kg (D) 60 kg 20. With the propagation of a

longi-tudinal wave through a material medium the quantities transmit-ted are—

(A) Energy

(B) Energy and linear momen-tum

(D) Energy and mass

21. Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K.

The piston of A is free to move while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in tempe-rature of the gas in B is—

(A) 30 K (B) 18 K (C) 50 K (D) 42 K 22. Rainbow is formed due to—

(A) Scattering and refraction (B) Total internal reflection and

dispersion

(D) Diffraction and dispersion 23. The displacement of particles in

a string in x-direction is repre-sented by y. Among the following expression for y, that describing wave motion is—

(A) cos kx sin ωt (B) k²x² – ω²t² (C) cos (k²x² – ω²t²) (D) cos² (kx + ωt)

24. Which of the following pheno-mena is not explained by

In document CSV Nov09 (Page 27-36)