Physics for jee

QUESTION BANK

PHYSICS

Gujarat Secondary and Higher

Secondary Education Board,

Gandhinagar

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Gujarat Secondary and Higher Secondary Education Board, Gandhinagar

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permitted without written permission of the Secretary, Gujarat Secondary and Higher Secondary Education Board, Gandhinagar.

Contribution

1 Dr. Hasmukh Adhiya (IAS) Principal Secretary , Education Department Gandhinagar 2 Shri R. R. Varsani (IAS) Chairman , G.S&H.S.E. Bord, Gandhinagar

3 Shri H. K. Patel (G.A.S) Dy. Chairman, G.S&H.S.E. Bord, Gandhinagar 4 Shri M. I. Joshi (G.E.S) Secretary , G.S&H.S.E. Bord, Gandhinagar

Coordination

1 Shri B. K. Patel O.S.D., G.S&H.S.E. Bord, Gandhinagar

2 Shri D. A.Vankar Assistant Secretary (Retd.), G.S&H.S.E. Bord, Gandhinagar 5 Shri G. M. Rupareliya Assistant Secretary, G.S&H.S.E. Bord, Gandhinagar

Expert Teachers

1. Shri J. M. Patel Shree J. M. Chaudhary Sarvajanik Vidhyalaya, Mehsana 2. Shri K. D. Patel J. N. Balika Vidhyalaya, Saraspur

3. Shri Mayur M. Raval P. J. Vakharia High School, Kalol 4. Shri S. G. Patel Sarkari Schook, Sector-12, Gandhinagar 5. Shri J. P. Joshi Diwan Ballubhai High School, Ahmedabad 6. Shri Vasudev B. Raval Vidhya Mandir High School, Palanpur 7. Shri Surendrabhai M. Rajkutir Convent of Jesus And Merry

8. Shri Sureshchandra H. Patel Alambic Vidhyalaya, Vadodara

9. Shri C. D. Patel Lalbahadur Shastri Vidhyalaya, Vadodara 10. Shri Mukesh N. Gandhi New English School, Nadiad

11. Shri Dineshbhai V. Suthar Retired Teacher

12. Shri S. S. Patel J. M. Chaudhary Sarvajanik Vidhyalaya, Mehsana 13. Shri Jayesh M. Purohit Ankur Vidhyalaya, Ahmedabad

14. Smt. Asha M. Patel Shree M.B. Vamdot Sarvajanik High School, Bardoli 15. Shri Maheshbhai Dhandhla Bhavnagar

16. Shri Mukesh M. Bhatt Bhavnagar 17. Shri Anilkumar Trivedi Anand

18. Shri Anand Thakkar Navchetan High School, Ahmedbad 19. Shri Sudhirkumar G. Patel Nutan High School, Visnagar 20. Smt. Anita Pillai Surat

P R E FA C E

engineering and medical courses after std-12. The burden of examinations on the side of the students was increasing day-by-day. For alleviating this difficulty faced by the students, from the current year, the Ministry of Human Resource Development , Government of India, has Introduced a system of examination covering whole country. For entrance to engineering colleges, JEE(Main) and JEE(Advanced) examinations will be held by the CBSE. The Government of Gujarat has except the new system and has decided to follow the examinations to be held by the CBSE.

Necessary information pertaining to the proposed JEE (Main) and JEE(Advanced) examination is available on CBSE website www.cbse.nic.in and it is requested that the parents and students may visit this website and obtain latest information – guidance and prepare for the proposed examination accordingly. The detailed information about the syllabus of the proposed examination, method of entrances in the examination /centers/ places/cities of the examinations etc. is available on the said website. You are requested to go through the same carefully. The information booklet in Gujarati for JEE( Main) examination booklet has been brought out by the Board for Students and the beneficieries and a copy of this has been already sent to all the schools of the state. You are requested to take full advantage of the same also However, it is very essential to visit the above CBSE website from time to time for the latest information – guidance . An humble effort has been made by the Gujarat secondary and Higher Secondary Education Boards, Gandhinagar for JEE and NEET examinations considering the demands of the students and parents , a question bank has been prepared by the expert teachers of the science stream in the state. The MCQ type Objective questions in this Question Bank will provide best guidance to the students and we hope that it will be helpful for the JEE and NEET examinations.

It may please be noted that this “Question Bank” is only for the guidance of the Students and it is not a necessary to believe that questions given in it will be asked in the examinations. This Question Bank is only for the guidance and practice of the Students. We hope that this Question Bank will be useful and guiding for the Students appearing in JEE and NEET entrance examinations. We have taken all the care to make this Question Bank error free, however, if any error or omission is found, you are requested to refer to the text – books.

M.I. Joshi R.R. Varsani (IAS)

I N D E X

Unit Unit Name GSEB NEET JEE Page

No. No.

PART - I

1 Phisycs & Measurement Y Y Y 1

2 Kinematics Y Y Y 21

3 Laws of Motion Y Y Y 51

4 Work, Energy and Power Y Y Y 78

5 Rotationl Motion Y Y Y 107

6 Gravitation Y Y Y 147

7 Properties of Solids and Liquids Y Y Y 195

8 Thermodynamics Y Y Y 258

9 Kinetic Theory of Gases Y Y Y 288

Unit-1

SUMMARY

• Measurement of large distance (Parallax Method) equation D = b

 where D = distance of the planet from the earth.

where  = parallax angle.

b = distance between two place of observation. • Measurement of the size of a planet or a star.

equation d

D

  where D = distance of planet from the earth, d = diameter of planet.

  angular diameter of planet. • Measurement of mass

The gravitational force on an object, of mass m, is called the weight of the object. 1 amu = 1.66  1027 _{kg = 1u}

• Estimation of Error

Absolute Error - Suppose the values obtained in several measurement of physical quantity

a are a₁, a₂, ... a_n If their arithmetic mean is a

then 1 2 1 .... 1 n n i i a a + a a a n n     

_

a₂, a_{2 ---} a_n are called absolute error • Average absolute error

1 2 1 ... 1          

_

Percentage error = a  100 % = a 100 %

a   • Combination of errors Addition Z = A + B    Z A B Substraction Z = A – B    Z A B Division Z = A B  Z A B Z A B      Multiplication Z = A • B  Z A B Z A B      Power Z = A  n Z n A Z A   

• Rule for determining number of significant figures • All the non - zero digits are significant

• All the zeros between two non zero digits are significant no matter where the decimal point is it at all.

• If the number is less then 1 then zeros on the right of decimal point but to the left of the first non - zero digit are not significant.

• In a number without decimal point the zeros on the right side of the last non zero digit are not significant.

• Dimensions and Dimensional formulas.

• The expression of a physical quantity with appropriate powers of M, L, T, K, A etc is called the dimensional formula of that physical quantity.

• The power of exponents of M, L, T, K, A are called dimensions of that quantity. • • Some important units of distance

–15 1 fermi (fm) 10 m o –10 1 A10 m 11 1 AU 1.496 10 m  15 1 light year9.46 10 m 16 1 par sec3.08 10 m

MCQ Questions

For the answer of the following questions choose the correct alternative from among the given ones.

Physics - scope and Excitement

- Physics, Technology and society. - Fundamental sources of nature. - Nature of Physical laws

1. Physics is one of the basic disciplines in the category of ... sciences. (A) Astro (B) Natural (C) Space (D) Genetic 2. ‘Physics’ comes from a ... word meaning nature

(A) Hindi (B) German (C) Greek (D) Sanskrit 3. Mechanics and newton’s motion laws as ... laws dependad.

(a) liner momentum (b) Energy conservation (c) Gravitational (d) Charge conservation 4. What is the approximate value of the Radious of a nucleus ?

(a) ₁₀–14_{m (b) 10}–31_{m (c) 10}–19_{m (d) 10}–15_m

5. The scope for ratio of length is in order to ... (a) –40

10 (b) 1040 (c) 1020 (d) 1030

6. The range of time scale is about ... (a) ₁₀–10_{sec to 10 sec}26 _{(c) 10}–15_{sec to 10 sec}15

(b) –22 18

10 sec to 10 sec (d) 20 25 10 sec to 10 sec

7. Birth, evolution and death of stars etc. are studid in branch of physics known as ... (a) Thermodynamics (c) Astro physics

(b) Quantam physics (d) Electronics

8. ... is a branch of physics in wich heat engine and refrigeratior efficiency is studied. (a) optics (b) Thermodynamics (c) Mechanics (d) Quantom physics 9. What is full name of LHC

(a) Large hadron collider (c) Large heavy cullent (b) Large hadron cullent (d) Light heavy cullent 10. The range of mass varies from ...

(a) ₁₀–15_{kg to 10 kg}26 _{(b) 10}–20_{kg to 10 kg}28 _{(c) 10}–30_{kg to 10 kg}55 _{(d) 10}–20_{kg to 10 kg}20

11. Length of Galaxies is in order of ... (a) 26

10 m (b) 36

10 m (c) 28

10 m (d) –14

10 m

12. The approximate value of charge of an electron is ...

(a) ₁₀–18_{c (b) 10}15_{c (c) 10}–38_{c (d) 10}–19_c

13. The universe is made up of ...

14. Nucleus of molecule is made up of wich fundamental constituents ? (a) only Electron (c) Electron and Proton (b) Proton and neutron (d) Electron and neutron

15. In the development of nenotechnology and biotechnology ... have played a vital role.

(a) ECG (b) ESR (c) NMR (d) AFM

16. What is full form of AFM ?

(a) Atomatic force mioroscope (c) Atomatic fire microscope (b) Atomic force mirror (d) Atomic force microscope 17. What is full name of ECG ?

(a) Electron cardiograph (c) Electron colour gram (b) Electro cardiograph (d) Electric colour graph 18. What is full name of ESR ?

(a) Electric space Radar (c) Electron spin Resonance (b) Electron space Range (d) Electric spin Resonance 19. What is full name of NMR ?

(a) Nuclear magnetic Resonance (c) Nuclear mega Radar (b) Neutron mega Resonance (d) Nuclear micro Radar 20. ... deals with electric charge and magnatic phenomenna

(a) Dynamics (b) Electro dynamic (c) Themodynamic (d) Mechanis 21. At present state, there are ... fundamental forces in nature.

(a) six (b) four (c) two (d) five

22. When charges are at rest the force is given by ... law.

(a) coulomb’s (b) Newton’s (c) Ampere’s (d) Faraday’s

23. The ... force is the force of mutual attraction between any two objects by virtue of their masses.

(a) Weak (b) Electromagnetic (c) Nuclear (d) Gravitational 24. The ... force is the strongest of all fundamental forces.

(a) nuclear (b) Electromagnetic (c) Gravitational (d) Weak nuclear 25. Electromagnetic force is ...

(a) attractive force only (c) repulsive force only (b) attractive and repulsive force (d) a short range force 26. Which of the following force binds The particle in the nucleons ?

(a) Electromagnetic force (b) Strong force (c) Gravitational force (d) Weak force 27. Electromagnetic force is ... range force

(a) Short (b) long (c) medium (d) very short 28. Quarks Quarks force is produced between

29. Which partical are emitted during the  decay from the nucleus ? (a) neutron and proton (c) electron and neutrino (b) electron and neutron (d) electron and proton 30. ... and ... law’s are called inverse square law

(a) Gravitation and weak (c) Coulomb’s and strong

(b) Gravitation and coulomb’s (d) Electromagnetic and coulomb’s 31. Which property of object is responsible for the electric force ?

(a) electric charge (b) pressure (c) volume (d) mass 32. Which property of object is responsible for the Gravitational force.

(a) electric charge (b) mass (c) pressure (d) volume 33. How much times is the strong nuclear force stronger then weak nuclear force ?

(a) 13

10 (b) 102 (c) 10–13 (d) 10–2

34. How much times is the strong nuclear force stronger then electro magnatic force ? (a) ₁₀13 _{(b) 10}2 _{(c) 10}–13 _{(d) 10}–2

35. How much times is the electromagnatic force stronger then Gravitational force (a) ₁₀13 _{(b) 10}–13 _{(c) 10}36 _{(d) 10}–36

36. Who has unified electromagnetism and optics ?

(a) Newton (b) Maxwell (c) Coulomb (d) Faraday 37. Who has unified terrestrial and celestial domains under a common law of Gravitational

(a) Newton (b) Maxwell (c) Coulomb (d) Farady

38. The weak nuclear force, Gravitational force and electromagnatic force are A, B and C Respectively then ...

(a) C > A > B (b) C > A < B (c) B > A > C (d) C < A < B 39. Range of weak nuclear force is ...

(a) ₁₀–15_{km (b) 10}–14_{km (c) 10}–18_{km (d) 10}–20_km

40. Strong nuclear force close not exist on ...

(a) Proton (b) nuclear (c) neutron (d) electron

41. The force acting between two point charges kept at a certain distance is F₁ Now magnitude of charge are double and distance between them is double. The force acting between them is F₂ find out the ratio of F₂/F₁ = ...

(a) 16 : 1 (b) 1: 16 (c) 1: 1 (d) 1: 8

42. If the resulting external force acting on system is zero then ... of the system is constant and if the resultant external torque acting on a system is zero then ... of the system is constart.

(a) total energy, angularmomentum (c) linermomentam, energy

43. Space is homogeneous and isotropic so ... law of servation is the result of this (a) linear and angular momentum (c) energy and charge

(b) angular and linear momentum (d) charge and energy

44. Time is homogeneous so ... law of conserbation is the result of this (a) angular momentum (b) linear momentum (c) energy (d) charge 45. The basic reason behind existance of which conseration of law is still not known ?

(a) angular momentum (c) energy (b) linear momentum (d) charge

46. The Gravitational force between any two body charges with distance as n

Fr where n = ...

(a) –1 (b) 2 (c) –3 (d) –2

47. Match the column

Column - I Column - II

(1) space is isotropic (P) conservation of linear momentum (2) space is homogeneous (Q) conservation of energy

(3) Time is homogeneous (R) conservation of charge still not known (4) Time is isotropic (S) conservation of angular momentam (a) 1- (S), 2-(P), 3-(R), 4-(Q) (c) 1-(P), 2-(S), 3-(R), 4-(Q) (b) 1-(S), 2-(P), 3-(Q), 4-(R) (d) 1-(R), 2-(Q), 3-(P), 4-(S)

Measurement and system of units

• Units of physical quantities, system of units, SI system of units, fundamental or Base units. precision in measurement. Error in measurement and significant figures.

• Dimensions and Dimensional formula, Dimensional analysis and its uses. 48. Which of the following unit is not of length ?

(a) light year (b) fermi (c) Ao (d) becquerel 49. becquerel is a ... unit and its symbol is ...

(a) supplementary, Bq (b) fundamental, Bq (c) derived, Bq (d) derived, Bv 50. How many fundamental units are there in SI system ?

(a) 5 (b) 7 (c) 6 (d) 4

51. Which of the following physical quantity is fundamental ?

(a) viscosity (b) velocity (c) force (d) time 52. Poise is the unit of

(a) viscosity (b) velocity (c) force (d) time 53. Which unit of physical quantity remains same for all unit system ?

54. Which of the following system of unit is not based on only units of mass length and time.

(a) SI (b) MKS (c) CGS (d) FPS

55. Which of the following symbol of unit does not follow practical norms for the use of SI system ?

(a) Kg (b) kg. (c) k (d) A

56. Why derive luminous intensity simbol form of SI system ?

(a) cd (b) Cd (c) cd. (d) CD

57. What is the ratio of 10 micron to 1 nenometer ? (a) ₁₀4 _(b) 3 10 (c) 16 10 (d) 15 10 58. _{1 0 0 n e n o m e te r}1 fe m to m e te r = ... (a) –6 10 (b) ₁₀–8 _{(c) 10}24 (d) ₁₀–24

59. If value of gravitational constant in MKS is

2 –11 2 Nm 6.67 10 kg  _{then value of G in} CGS = ... 2 2 dyn cm gm  (a) –9 6.67 10 (b) –7 6.67 10 (c) –8 6.67 10 (d) –5 6.67 10

60. A partical has an acceleration of 72 km / min2 _{find acceleration in SI system.}

(a) 2 0.5 m / s (b) 2 30 m / s (c) 2 18 m / s (d) 2 20 m / s 61. 950 dyne = ... newton (a) _{9.5 10} –3 _{(b) 95 10} –5 _{(c) 950 10} –7 _{(d) 9.5 10} –4 62. 100 picometer = ... (a) –8 10 cm (b) –7 10 m (c) –6 10 10 m (d) –8 10 10 m

63. 100 walt hour = ... joule.

(a) _{3.6 10 J} 5 _{(b) 3.6 10 J} 6 _{(c) 36 10 J} 5 _{(d) 36 10 J} 6

64. If x meter is a unit of length then area of 1m2 _{= ...}

(a) x (b) x2 _{(c) x}–2 _{(d) x}–1

65. 1 Mev = ... ev

(a) ₁₀7 _{(b) 10}4 _{(c) 10}5 _{(d) 10}6

66. Wave length of light radiation 0.000015 m = ...

(a) 15 micron (b) 1.5 micron (c) 150 micron (d) 0.15 micron 67. ₁0 _{= ...} (a) _{600 ''} (b) _{3600 ''} (c) _{180 ''} (d) _{3600 '} 68. 1 rad = ... (a) 0 180 (b) 3.140 (c) 0 180    _    (d) 0 180       

69. 1 g = ... amu

(a) _{6.02 10} 23 _{(b) 6.02 10} –23 _{(c) 1.66 10} –27_{(d) 1.66 10} 27

70. 1 parsec = ...

(a) ₁₀–15_{m (b) 1.496 10 m} 11 _{(c) 1.496 10 m} 15 _{(d) 3.08 10 m} 16

71. Which of the following unit does not represent the unit of power ? (a) ampere/volt (c) (ampere)2 _{ ohm}

(c) joule/second (d) ampere  volt

72. Write the unit of angular acceleration in the SI system.

(a) N.Kg (b) _{rad / (sec)}2 _{(c) m/sec (d) N/kg}

73. unit of universal gravitational constant is ...

(a) _{kg m sec}–1 _{(b) N m sec}–1 _{(c) N m kg}2 –2 _{(d) N m kg}–1

74. The unit of stefen Boltzman constant () is ...

(a) _{w m}2 –2_k–1 _{(b) w m k}2 –3 _{(c) w m}–2_k4 _{(d) w m}–2_k–4

75. Unit of momentum physical quantity ?

(a) newton - second (b) newton/second (c) Jule (d) Jule/second 76. Light year is a unit of ...

(a) Mass (b) volume (c) density (d) Distance 77. Joule/seed is the unit of ...

(a) Work (b) angular momentum (c) Pressure (d) Energy 78. The SI unit of momentum is ...

(a) kg newton (b) –2 2

kg m s (c) –1

kg m (d) –1

kg ms

79. Volt/meter is the unit of ...

(a) Work (b) viscosity (c) Electric fild intensity (d) velosity 80. The force F is represented by equation F = _P1 _{+ Q}

, where  is the length. The unit of P is same as that of ...

(a) Surface tension (b) velocity (c) force (d) momentum 81. Write the unit of surface tension in SI system.

(a) N₂ m (b) N m (c) 2 dyne cm (d) dyne cm

82. Which physical quantity has unit of pascal - secod ?

(a) Velocity (b) viscocity (c) energy (d) coefficient of viscocity 83. Which physical quantity has unit of joule - second ?

84. What is the least count of vernier callipers ? (a) –4

10 m (b) 10 m–5 (c) 10 m–2 (d) 10 m–3

85. What is the least count of screw gauge ?

(a) _{10 m}–4 _{(b) 10 m}–5 _{(c) 10 m}–2 _{(d) 10 m}–6

86. For measurement of astronomical distance ... is used.

(a) vernier callipers (b) spherometer (c) screwgauge (d) indirect method 87. Which mictoscope is used to measure the dimension of particle having dimension less than

0 4000 A ?

(a) electron microscope (b) simple microscope (c) optical microscope (d) none of above 88. In electron microscope electron behave like ...

(a) charge (b) mass (c) particles (d) wave 89. Which wave length of light is used in an optical microscope ?

(a) radiowave (b) X - ray (c) infrared (d) visible

90. The intercepted area of the spherical surface about the center is 0.25m2 _{having diameter 50}

cm what will be solid angle ? (a) –1

4 10 sr (b) 3

1 10 sr (c) –1

10 sr (d) –1

5 10 sr

91. One planet is observed from two diametrically opposite point A and B on the earth the angle subtended at the planet by the two directions of observations is 1.8o. Given the diameter of the earth to be about 7

1.276 10 m . What will be distance of the planet from the earth ? (a) _{40.06 10 m} 8 _{(b) 4.06 10 m} 8 _{(c) 400.6 10 m} 13 _{(d) 11 10 m} 8

92. Find the distance at which 4 AU would subtend an angle of exactly _1" of arc.

11 16

[1AU 1.496 10 m,1" 4.85 10 rad]   

(a) _{1.123 10 m} 5 _{(b) 11.23 10 m} 5 _{(c) 1.123 10 m} 17 _{(d) 11.23 10 m} 17

93. The percentage error in the distance 1005 cm is ...

(a) 5 % (b) 6% (c) 8 % (d) 20 %

94. In an experiment to determine the density of a cube the percentage error in the measurement of mass is 0.25 % and the percentage error in the measurement of length is 0.50 % what will be the percentage error in the determination of its density ?

(a) 2.75 % (b) 1.75 % (c) 0.75 % (d) 1.25 % 95. If _Ab4 _{the fractional error in A is ...}

(a)









 where percentage error in A , B and C are respectively 2 % 3% and 5 %  then total percentage error in measurement of p

97. In the experiment of simple pendulum error in length of pendulum ( ) is 5 % and that of g is 3 % then find percentage error in measurement of periodic time for pendulum

(a) 4.2 % (b) 1.2 % (c) 2 % (d) 4 % 98. Acceleration due to gravity is given by 2

GM g

R

 what is the equation of the fractional error g / g

in measurement of gravity g ? [G & M constant] (a) – R R  (b) 2 R R  (c) –2 R R  (d) 1 R 2 R 

99. The period of oscillation of a simple pendulum is given by T 2 _g what is the equation of the relative error T

T  in measurement of period T ? (a) 1 2   (b) 2   (c) 1 4   (d) 4  

100. The length of a rod is (10.150.06) cm what is the length of two such rods ?

(a) (20.300.06) cm (b) (20.30 1.6) cm (c) (10.300.12) cm (d) (20.300.12) cm

101. For a sphere having volume is given by V 4 r3 3

  What is the equation of the relative error

V V 

in measurement of the volume V ?

(a) 3 r r  (b) 4 r r  (c) 4 r 3 r  (d) 1 r 3 r 

102. Kinetic energy K and linear momentum P are related as

2 p K

2m

 . What is the equation of the

relative error k

k 

in measurement of the K ? (mass in constant)

(a) p p  (b) p 2 p  (c) p 2 p (d) p 4 p 

103. Heat produced in a current carrying conducting wire is H = I2Rt it percentage error in I, R and t is 2 % , 4 % and 2 % respectively then total percentage error in measurement of heat energy ...

(a) 8 % (b) 15 % (c) 5 % (d) 10 %

104. The resistance of two resistance wires are R1(1005) and R2(2007) are connected

in series. find the maximum absolute error in the equivalent resistance of the combination. (a) 35  (b) 12  (c) 4  (d) 9 

105. The periodic time of simple pendulum is T 2 g

   relative error in the measurement of T and

 are a and b respectively find relative error in the measurement of g

106. A physical quantity x is given by x = 4 3 1 4 4 3 A B

C D due to which physical quantgity produced the

maximum percentage error in x

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

107. The resistance R V I

 where V 100 5 volts and I 10 0.3 anperes calculate the percentage error in R.

(a) 8 % (b) 10 % (c) 12 % (d) 14 % 108. The number of significant figures in 0.000150 is ...

(a) 3 (b) 5 (c) 2 (d) 4

109. Which of the following numerical value have significant figure 4 ?

(a) 1.011 (b) 0.010 (c) 0.001 (d) 0.100 110. What is the number of significant figures in 3

5.50 10 ?

(a) 2 (b) 7 (c) 3 (d) 4

111. The mass of substance is 75.5 gm and its volume is 25 cm2_{. It’s density up to the correct}

significant figure is ... (a) 3 3.02 gm / cm (b) 3 3.200 gm / cm (c) 3 3.02 gm / cm (d) 3 3.1 gm / cm

112. The area of a rectangle of size 1.25 2.245 cm in significant figure is ...

(a) _{2.80625 cm}2 _{(b) 2.81 cm}2 _{(c) 2.806 cm}2 _{(d) 2.8062 cm}2

113. The significant figures in 500.5000 are ...

(a) 5 (b) 3 (c) 7 (d) 6

114. Addition of measurement 15.225 cm, 7.21 cm and 3.0 cm in significant figure is ... (a) 25.43 cm (b) 25.4 cm (c) 25.435 cm (d) 25.4350 cm 115. Substract 0.2 J from 7.36 J and express the result with correct number of significant figures.

(a) 7.160 J (b) 7.016 J (c) 7.16 J (d) 7.2 J 116. After rounding of the number 9595 to 3 significant digits the value becomes ...

(a) 9600 (b) 9000 (c) 9590 (d) 9500 117. How many significant numbers are there in 5

(2.304.70) 10 ?

(a) 3 (b) 4 (c) 2 (d) 5

118. The radius of circle is 1.26 cm. According to the concept of significant figures area of it can be represented as -(a) 2 4.9850 cm (b) 2 4.985 cm (c) 2 4.98 cm (d) 2 9.98 cm

119. If A = 3.331 cm B = 3.3 cm then with regard to significant figure A + B = ... (a) 6.6 cm (b) 6.31 cm (c) 6.631 cm (d) 6 cm

120. If the length of rod A is (2.350.01) cm and that of B is (5.680.01) cm then the rod B is longer than rod A by ...

(a) (2.430.00) cm (b) (3.330.02) cm (c) (2.430.01) cm (d) (2.430.001) cm

121. In acceleration, The dimensions for mass ... for length .. and for time (a) 0,1,–2 (b) 1,0,–2 (c) –2,0,1 (d) –2,1,0 122. Dimensional formula for power is ...

(a) 2 –2 –3

M L T (b) M L T1 2 –2 (c) M L T1 3 –1 (d) M L T0 2 –2

123. Dimensional formula for calories is ...

(a) _{M L T}1 1 –2 _{(b) M LT}2 1 –2 _{(c) M L T}1 2 –2 _{(d) M L T}2 2 –2

124. Dimensional formula for thermal conductivity (k) is .. (a) 2 1 –2 –1

M LT K (b) M LT K1 1 –2 1 (c) M L T K1 0 –3 –1 (d) M L T K1 1 –3 –1

125. Dimensional formula for Resistance (R) is ... (a) 1 1 –3 –1

M L T A (b) M LT A1 1 0 –1 (c) M L T A1 2 –3 –2 (d) M L T A1 0 –3 –1

126. Dimensional formula for conductance is ... (a) –1 2 –3 2

M L T A (b) M L T A1 2 –2 1 (c) M L T A1 –2 3 2 (d) M L T A–1 –2 3 2

127. Which physical quantity is represented by 1 3 –3 2 M L T A ?

(a) Resistivily (b) Resistance (c) conductance (d) conductivity 128. Which physical quantity is represented by –1 –3 3 2

M L T A ?

(a) Resistivity (b) Resistance (c) conductance (d) conductivity 129. Which physical quantity is represented by 1 1 –3 –1

M L T A ?

(a) Stress (b) Resistance (c) Electricfield (d) potential Difference 130. The dimensional formula of plank’s constant is ...

(a) _{M L T}3 2 –1 _(b) 1 2 –1

M L T (c) _{M L T}2 1 –1 _{(d) M L T}1 2 –3

131. Dimensional formula of latent heat is ...

(a) _{M L T}0 2 –2 _{(b) M L T}2 0 –2 _{(c) M L T}1 2 –1 _{(d) M L T}2 2 –1

132. Dimensions of impulse are.

(a) _{M L T}–1 –1 1 _{(b) M LT}1 1 –1 _{(c) M LT}1 1 1 _{(d) M L T}1 2 –2

133. Write dimensional formula of coefficient of viscosity (a) 1 2 –1

M L T (b) M LT–1 1 1 (c) M L T1 –1 –1 (d) M LT1 1 –1

134. Dimensional formula for torque is (a) 2 2 –3

M L T (b) M L T2 1 –2 (c) M L T1 1 –2 (d) M L T1 2 –2

135. Dimensional formula for capisitance (C)

136. Dimensional formula for Boltzmann’s constant is ... (a) 1 1 –2 –1

M L T K (b) M LT K2 1 –2 –1 (c) M L T K1 2 –2 –1 (d) M L T K2 2 1 –2

137. Dimensional formula for electromotive force (emf) (a) 2 1 –1 –3

M LT K (b) M L T K1 2 –3 –1 (c) M L T K1 1 –3 –1 (d) M L T K1 2 3 –1

138. Which physical quantity has dimensional formula as CR where C - capisitance and R - Resistance ? (a) Frequency (b) current (c) Time period (d) acceleration 139. Write the dimensional formula of the ratio of linear momentum to angular momentum.

(a) 0 –1 0

M L T (b) M L T1 1 0 (c) M LT0 1 0 (d) M L T0 1 1

140. If L and R are respesented as the inductance and resistance respectively then the dimensional formula of R

L will be ...

(a) –2 1 –2 1

M L T A (b) M L T A0 0 –1 0 (c) M L T A1 –1 0 1 (d) M L T A1 3 1 0

141. Write the dimensional formula of r.m.s (root mean square) speed.

(a) _{M L T}1 2 –2 _{(b) M L T}0 2 –2 _{(c) M LT}0 1 –1 _{(d) M L T}1 0 –1

142. One physical quantity represented by an equation as (p – q)c 2



where p, q and c are length then quantity is ..

(a) length (b) velocity (c) Area (d) volume 143. The dimensional formula of magnetic flux is ...

(a) 1 2 –2 –1

M L T A (b) M L T A1 2 1 2 (c) M L T A1 2 –2 2 (d) M L T A–1 –2 1 2

144. Which physical quantity has unit of pascal - second ?

(a) Force (b) Energy (c) Coefficient of viscocity (d) velocity 145. Dimensional formula of CV ? where C - capacitance and V - potential different

(a) 1 –2 4 2

M L T A (b) M L T A1 2 –3 1 (c) M L T A0 0 1 –1 (d) M L T A0 0 1 1

146. The equation of a wave is given by Y A sin x–k v

 

 _{  }

 

where  is the angular velocity and

v is the linear velocity. Write the dimensional formula of K

(a) _{M L T}0 0 1 (b) _{M L T}1 0 –1 (c) _{M L T}0 1 1 (d) _{M L T}1 –1 1

147. If P and q are diffrent physical quantities then which one of following is only possible dimensionally ? (a) p + q (b) p q (c) p – q (d) p = q 148. From p a₂





  constant equation is dimensionally correct find the dimensional formula

for b ? where P = preasure V = volume (a) _{M L T}0 3 0 _(b) 1 3 0

M L T (c) _{M L T}0 1 3 _(d) 1 1 –1 M L T

149. Pressure P = A cosBx + c sinDt where xin meter and t in time then find dimensional formula of D

B

(a) 1 1 –1

M LT (b) M LT0 1 –1 (c) M L T1 1 0 (d) M L T–1 0 1

150. Find the dimensional formula for energy per unit surface area per unit time (a) 1 0 –2

M L T (b) M LT0 1 –1 (c) M L T1 0 –3 (d) M L T1 –1 1

151. Equation of force _Fatbt2 _{where F is force in Newton t is time in second, then write unit}

of b. (a) _Nm–1 _{(b) Nm}2 _{(c) Nm (d) Nm}–2 152. Pressure 2 at P bx

 where x = distance, t= time find the dimensional formula for a

b

(a) _{M L T}1 0 –4 _{(b) M LT}1 1 –1 _{(c) M L T}1 0 –2 _{(d) M L T}1 0 –2

153. _{– Bxt}2

0

FA (1 – e ) where F is force and x is desplacement. write the dimension formula of B

(a) _{M LT}2 1 –1 _{(b) M L T}0 –1 –2 _{(c) M L T}1 0 –2 _{(d) M L T}1 2 –1

154. Equation of physical quantity 2 at bt  

v where v = velocity t = time so write the dimensional formula of a in this equation

(a) _{M LT}0 1 –1 _{(b) M LT}1 1 –1 _{(c) M LT}0 1 –2 _{(d) M L T}1 2 0

155. Density of substance in CGS system is 3.125 3

gm / cm what is its magnitude is SI system ? (a) 0.3125 (b) 3.125 (c) 31.25 (d) 3125

156. The resistivity of resistive wire is AR

L

  where L = length of wire A = Area of wire and

R is resistance of wire find dimension formula of  (a) 1 3 –3 –2

M L T A (b) M L T A1 2 –3 –2 (c) M L T A2 3 1 2 (d) M L T A2 3 –3 –2

157. A cube has numerically equal volume and surface area calculate the volume of such a cube. (a) 2000 Unit (b) 216 Unit (c) 2160 Unit (d) 1000 Unit 158. Which out of the following is dimensionally correct.

(a) p2 _{= hg (b) p = h}2_{g (c) p = hg (d) p = h}2_g

159. If energy _{EG h c}p q r _{where G is the universal gravitational constant. h is the plank’s constant}

and c is the velocity of light, then the values of p, q and r are respectively

(a) – , ,1 1 5 2 2 2 (b) 1 1 5 , , 2 2 2 (c) 5 1 1 , , – 2 2 2 (d) 1 1 5 , – , 2 2 2

160. If the centripetel force is of the form mavbrc find the values of a, b and c

161. equation of _t ₀[1 (T₂ –T₁)] find out the dimensions of the coefficient of linear expansion

 suffix.

(a) _{M L T K}0 0 1 1 _{(b) M LT K}0 1 1 1 _{(c) M LT K}1 1 0 1 _{(d) M L T K}0 0 0 –1

162. Test if the following equation are dimensionally correct (S = surface tension  = density P = pressure v = volume n = coefficient of viscocity r = redious)

(a) h2Scos_rg  (b) v  p  (c) 4 pr t v 8n    (d) all correct

163. Match list - I with list - II

List - I List - II

(1) Joule (a) henry  ampere/sec

(2) Walt (b) coulomb  volt

(3) volt (c) metre  ohm

(4) Resistivity (d) (ampere)2

 ohm

(a) b,d,c,a (b) c,a,b,d (c) b,d,a,c (d) b,c,a,d 164. Match column - I with column - II

Column -I Column - II (1) capacitance (a) 1 1 –3 –1 M L T A (2) Electricfield (b) 1 2 –1 M L T (3) planck’s constant (c) –1 –2 4 2 M L T A (4) Angular momentum (d) 1 2 –1 M L T

(a) a,c,b,d (b) c,a,d,b (c) c,a,b,d (d) a,b,d,c

165. In the relation – P e ,      B z k

P is pressure, z is distance, k is boltz mann constant and  is the temperature. The dimensional formula of B will be

(a) 0 2 0

M L T (b) 1 0 1

M L T (c) 1 1 –1

1(B)

26(B)

51(D)

76(D)

101(A)

126(D)

151(D)

2(C)

27(B)

52(A)

77(B)

102(B)

127(A)

152(A)

3(C)

28(A)

53(B)

78(D)

103(D)

128(D)

153(B)

4(A)

29(C)

54(A)

79(C)

104(B)

129(C)

154(C)

5(B)

30(B)

55(B)

80(A)

105(C)

130(B)

155(D)

6(B)

31(A)

56(A)

81(B)

106(C)

131(A)

156(A)

7(C)

32(B)

57(A)

82(D)

107(A)

132(B)

157(B)

8(B)

33(A)

58(B)

83(B)

108(A)

133(C)

158(C)

9(A)

34(B)

59(C)

84(A)

109(A)

134(C)

159(A)

10(C)

35(C)

60(D)

85(B)

110(C)

135(D)

160(B)

11(A)

36(B)

61(A)

86(D)

111(D)

136(A)

161(D)

12(D)

37(A)

62(C)

87(A)

112(B)

137(B)

162(D)

13(D)

38(A)

63(A)

88(D)

113(C)

138(C)

163(C)

14(B)

39(C)

64(C)

89(D)

114(B)

139(A)

164(B)

15(D)

40(D)

65(D)

90(A)

115(D)

140(B)

165(B)

16(D)

41(C)

66(A)

91(B)

116(C)

141(C)

17(B)

42(B)

67(B)

92(C)

117(A)

142(C)

18(C)

43(A)

68(C)

93(A)

118(C)

143(A)

19(A)

44(C)

69(A)

94(B)

119(A)

144(C)

20(B)

45(D)

70(D)

95(C)

120(B)

145(D)

21(B)

46(D)

71(A)

96(C)

121(A)

146(A)

22(C)

47(B)

72(B)

97(D)

122(B)

147(B)

23(D)

48(D)

73(C)

98(B)

123(C)

148(A)

24(A)

49(A)

74(D)

99(A)

124(D)

149(B)

25(B)

50(B)

75(A)

100(D)

125(C)

150(C)

HINT

= [ M+ 3 l ] 100 M l         = 1.75 % 96 2 3 A B P C  P A B C % [2 3 ] P A B C        = 21 % 97 T 2 l g   T 1 l 1 g 100 [ ] 100 T 2 l 2 g          = 4 %

100 length of two rods2l

= 2(10.150.06) = (20.300.12) cm 103 2 heat energy H = I RT H I R T 100 [2 ] 100 H I R T          = 10 % 105 g 4 2 2 T   l g l T 2 g l T       = b + 2q 33 Strong nuclear force

Electronmagnaticforce = 2 1

10 = 10

2

34 Strong nuclear force

Weak nuclear force = -13 1 10 = 10 13 35 Electronmagnetic force Gravational force = -2 -38 10 10 = 10 36 41 1 12 2 1 kq q F r  ' ' 1 2 2 2 2 kq q F r  49 –6 4 –9 10 10 10 10   58 –15 –8 –9 10 10 100 10  60 72 72 1000 20 ₂ min 3600 (sec) km  m   2 ( ) 64 Area = _2 A = x m2 2 2 –2 2 2 A 1 1 m x x x    69 1 amu = _{1.66 10} –27_kg = _{1.66 10} –24_gm 23 1gm6.023 10 amu 80 1 –1 Fp q |1 p_ _F F N(Neuton) P surface tension (meter)      90 2 A 0.025 m   2r0.5m 2 A Solid angle 0.4 Sr r   = =_{4 10 Sr} –1

107 Resis tan ce R V I  R V I R V I      R 5 0.3 R 100 10    R 8 R 100   R % 8% R   111 density mass 75.5 volume 25 = = 3.02 = 3 3.1 g / cm

128 Re sistivity Resis tan ce Area length   129 Electricfield force electric ch arg e  130 2 mass (dis tan ce) plank 's cons tan t

time  

131 latent heat Q heat energy mass ( ) =

133 2

Force time coefficientof vis cos ity

(length)  

141 2

Urms u root mean square speed

142 If p = q = c = L then (p - q)c = L2 _{= Area} 144 d If F = nA dx F n = pascal second d dx  v v A = 146 yA sin ( x – k) v x k   v 0 0 1 x k M L T v 148 2 a P (v – b) cons tan t v         2 PV – Pb a – ab constant v v   PV – Pb  0 3 0 V b M L T   

149 cos Bxdim ensionl less 0 0 0 BxM L T 0 0 0 0 –1 0 M L T B M L T X   Same as 0 0 –1 DM L T 0 1 –1 D M L T B   151 _Fatbt2 2 Fbt at 2 2 F N b t m   153 _{– Bxt}2 FA (1 – e ) 2 Bxt dimensional less 0 0 0 0 –1 –2 2 M L T B M L T xt   155 Density 3.125 gm₃ cm  = = –3 –6 3 3.125 10 kg 10 m  = 3125 _{kg / m}3 157 _{volume of cube Va}3 2 total surface area of cube A = 6a

V A   3 2 a 6a a6 3 V (6) 216 unit   

159 P q r EG h c 1 2 –2 EM L T –1 3 –2 GM L T 1 2 –1 hM L T 0 1 –1 cM L T take it 1 2 –2 –1 3 –2 p 1 2 –1 q (M L T )(M L T ) (M L T ) 0 1 –1 c (M L T ) = –p q 3p 2q r –2p–q–r M  L  T 1 1 5 P , q , r 2 2 2     160 a b c Fm v r 1 1 –2 FM L T 0 1 –1 M L T  v 0 1 0 rM L T 1 0 0 mM L T take it 1 1 –2 1 a 1 –1 b 1 c (M L T )(M ) (L T ) (L ) = a b c – b M L T a 1, b 2, c –1     165 z M L T0 0 0 kB    kB z    and P =  u kB p pz      0 2 0 M L T 

Unit - 2

Kinematics

SUMMARY

t     • Velocity = displacement r time t

v

Ins tan eous velocity υ lim

t dt          

• Average acceleration Gave t    • t υ dυ Ins tan tan eous acceleration a lim

t dt         

• Equation for Uniformally accelerated motion (1) _υ = _υ0 + at (3) o 2 1 d = t + at 2  (2) s Vo V t 2         (4) V 2 _{= Vo}2 _{+ 2ad} • th n o a

Dis tan ce covered in n Second S V (2n –1) 2   • About Vectors A  . _B = AB cosq _A ´ _B = AB sinq nˆ A  _. A  ₌ 2 |_A | _A ´ _A = 0

ˆi . _ˆi = ˆj . ˆj = _kˆ . _ˆi = 1 _ˆi ´ _ˆi = _ˆj ´ ˆj = ˆ_k ´ _kˆ = 0 ˆi . ˆj = ˆj . _kˆ = _kˆ . _kˆ = 0 _ˆi ´ ˆj = K _ˆj ´ _kˆ = _{ˆi ˆk} ´ _ˆi = _ˆj

cosq = A. B AB   A  _´ B  = ˆ ˆ ˆ A A A B B B i j k x y z x y z

A  ^_B then _A ._B = 0 _A ^_B then |_A ´ _B | = AB A  || _B then _A ._B = AB _A ||_B then _A ´ _B = 0

|_A |= |_B | and _A and _B is Q the angle between

(1)

_θ

_θ

_θ

_θ

_θ

- Time to reach the highest point tm υ sino g   - Maximum height H = 2 0 2 υ s in 2 θ g - Range R = υ sin 220 θ g - Maximum Range 2 0 υ R g 

- Flight time T 2υ sino g   - Equation of trajectory 2 2 2 o gx y x tan – 2 cos     - R4H cot

MCQ

For the answer of the following questions choose the correct alternative from among the given ones.

(1) A branch of physics dealing with motion without considering its causes is known as .... (A) Kinematicas (B) dynamics

(C) Hydrodynemics (D) mechanics (2) Mechanics is a branch of physics. This branch is ...

(A) Kinematics without dynamics (B) dynamics without Kinematics (C) Kinematics and dynamics (D) Kinematics or dynamics (3) To locate the position of the particle we need ...

(A) a frame of referance (B) direction of the particle (C) size of the particle (D) mass of the particle

(4) Frame of reference is a ... and a ... from where an obeserver takes his observation, (A) place, size (B) size, situation

(C) situation, size (D) place, situation (5) -2 B -1 0 1 2 3 A (m)

As shown in the figure a particle moves from 0 to A, and then A to B. Find pathlength and displacement.

(A) 2m, –2m (B) 8m, –2m (C) 2m, 2m (D) 8m, –8m

(6) A particle moves from A to B and then it moves from B to C as shown in figure. Calculate the ratio between path lenghth and displacement.

(A) 2 (B) 1 (C) 1

2 (D) 

(7) A particle moves from A to P and then it moves from P to B as shown in the figure. Find path length and dispalcement.

600 P (A) 2 3 l , l (B) 3

l

l

(8) A car goes from one end to the other end of a semicircular path of diameter ‘d’. Find the ratio between path legth and displacement.

(A) 3

2 

(B)  (C) 2 (D) π

2

(9) A particle goes from point A to B. Its displacement is X and pathlength is y. So x

y ...

(A) > 1 (B) < 1 (C) 1 (D) 1

(10) As shown in the figure a partricle statrs its motion from 0 to A. And then it moves from A to B. _AB is an arc find the Path length

O r 3  (A) 2r (B) r 3   (C) _ _   π r 1 + 3 (D) 3





(11) Here is a cube made from twelve wire each of length l. An ant goes from A to G through path A-B-C-G. Calculate the displacement.

  G E F H (A) 3l (B) 2l (C) _3l (D) l 3

(12) As shown in the figure particle P moves from A to B and particle Q moves from C to D. Desplacements for P and Q are x and y respectivey then

5 4 3 2 1 1 2 3 4 5 O (A) x > y (B) x < y (C) x = y (D) x y

(13) Shape of the graph of position  time given in the figure for a body shows that

t x

o

(A) The body moves with constant acceleration (B) The body moves with zero velocity

(C) The body returns back towards the origin (D) nothing can be said

(14) The graph of position  time shown in the figure for a particle is not possible because ...

t x

o

(A) velocity can not have two values on one time (B) Displacement can not have two values at one time (C) Acceleration can not have two values at one time (D) A, B and c are true

(15) An ant goes from P to Q on a circular path in 20 second Raidus OP = 10m. What is the average speed and average velocity of it ?

120 0 p O R (A) ms , 3 ms–1 –1 6  (B) 3  –1 3 –1 ms , ms 2 (C) ms , 3 ms–1 –1 3  (D) –1 –1 ms , 6 ms 

(16) A particle is thrown in upward direction with initial velocity of 60 m/s. Find average speed and average velocity after 10 seconds. [g = 10 ms–2_]

(A) 26ms–1_{, 16ms}–1 _{(B) 26ms}–1_{, 10ms}–1

(17) The ratio of pathlength and the resepective time interval is (A) Mean Velocity (B) M ean speed (C) intantaneous velocity (D) intantaneous speed

(18) A car moving over a straight path covers a distance x with constant speed 10 ms–1 _{and then}

the same distance with constant speed of V₂. If average speed of the car is 16ms–1_{, then V} 2 = ....

(A) 30 ms–1 _{(B) 20 ms}–1 _{(C) 40 ms}–1 _{(D) 25 ms}–1

(19) A bus travells between two points A ans B. V₁ and V₂ are it average speed and average velocity then

(A) v₁ > v₂ (B) v₁ < v₂ (C) v₁ = v₂ (D) depends on situation (20) A car covers one third part of its straight path with speed V₁ and the rest with speed V₂. What

is its average speed ?

(A) 1 2 1 2 3 2 v v v v (B) 1 2 1 2 2 3 v v v  v (C) 1 2 1 2 3 2 v v v  v (D) 1 2 1 2 3 2 2 v v v  v

(21) Rohit completes a semicirular path of radius R in 10 seconds. Calculate average speed and average velocity in ms–1_. (A) 2 R 2R, 10 10  (B) R R, 10 10  (C) πR 2R, 10 10 (D) 2 R R , 10 10 

(22) A particle moves 4m in the south direction. Then it moves 3m in the west direction. The time taken by the particle is 2 second. What is the ratio between average speed and average velocity ? (A) 5 7 (B) 7 5 (C) 14 5 (D) 5 14

(23) A particle is projected vertically upwards with velocity 30ms–1_{. Find the ratio of average speed}

and instantaneous velocity after 6s. [g = 10ms–1_]

(A) 1

2 (B) 2 (C) 3 (D) 4

(24) The motion of a particle along a straight line is described by the function x = (3t – 2)2_{. Calculate}

the acceleration after 10s.

(A) 9ms–2 _{(B) 18mls (C) 36ms}– _{(D) 6ms}–

(25) Given figure shows a graph at acceleration  time for a rectilinear motion. Find average acceleration in first 10 seconds.

o t 15 10 5 10 2 m a S       (A) 10ms–2 _{(B) 15ms}–2 _{(C) 7.5ms}–2 _{(D) 30ms}–2

(26) A body starts its motion with zero velocity and its acceleration is 3m/s2_{. Find the distance travelled}

by it in fifth second.

(27) A body is moving in x direction with constant acceleration  . Find the difference of the displacement covered by it in nth second and (n–1)th second.

(A) α (B)

2 

(C) 3 (D) 3

2

(28) What does the speedometer measure kept in motorbike ? (A) Average Velocity (B) Average speed

(C) intantaneous speed (D) intantaneous Velocity

(29) The displacement of a particle in x direction is given by x = 9 – 5t + 4t2_{. Find the Velocity}

at timt t = 0

(A) –8 ms–1 _{(B) –5 ms}–1 _{(C) 3 ms}–1 _{(D) 10 ms}–1

(30) A freely falling particle covers a building of 45m height in one second. Find the height of the point from where the particle was released. [g = 10ms–2_]

(A) 120m (B) 125m (C) 25m (D) 80m

(31) The distance travelled by a particle is given by s = 3 + 2t + 5t2 _{The initial velocity of the particle}

is ...

(A) 2 unit (B) 3 unit (C) 10 unit (D) 5 unit

(32) A particle is thrown in upward direction with Velocity V₀. It passes through a point p of height h at time t₁ and t₂ so t₁ + t₂ = .... (A) 0 g v (B) 2v0 g (C) 2h g (D) h 2g

(33) A particle is thrown in upward direction with initial velocity V₀. It crosses point P at height h at time t₁ and t₂ so t₁t₂ = _______ (A) 2h g (B) 2 0 V 2g (C) 2 0 2V g (D) h 2g

(34) Ball A is thrown in upward from the top of a tower of height h. At the same time ball B starts to fall from that point. When A comes to the top of the tower, B reaches the ground. Find the the time to reach maximum height for A.

(A) h g (B) 2h g (C) h 2g (D) 4h g

(35) In the figure Velocity (V)  position graph is given. Find the true equation.

xo X Vo V (A) 0 0 0 x – x v v v (B) 0 0 0 – x x v v v (C) 0 0 0 – x – x v v  v (D) v v0 v 0 0 = x + x

(36) In the figure there is a graph of ax for a moving particle. Hence da = dt .... V xo X a a_o o (A) 0 0 x a (B) 0 0 –x a (C) 0 0 –a x (D) 0 0 a x

(37) A particle is moving in a straight line with intial velocity of 10 ms–1_{. A graph of acceleration  time of the}

particle is given in the figure. Find velocity at t = 10 s.

o

10 5

a

(A) 25 ms–1 _{(B) 35 ms}–1 _{(C) 45 ms}–1 _{(D) 15 ms}–1

(38) A graph of moving body with constant acceleration is given in the figure. What is the velocity after time t ? o t A V D B C E t 1 (A) 0A + DC0E BC (B) DC 0A + DE BC (C) BC AB + 0E DC (D) DC 0A + AD BC (39) t V o

The graph given in the figure shows that the body is moving with ...

(A) increasing acceleration (B) decreasing acceleration

(40) Slope of the velocity-time graph gives of a moving body..

(A) displacement (B) acceleration (C) initial velocity (D) final velocity (41) The intercept of the velocity-time graph on the velocity axis gives.

(A) initial velocity (B) final velocity (C) average velocity(D) instanteneous velocity (42) Here are the graphs of velocity  time of two cars A and B, Find the ratio of the acceleration

after time t. t V 130 60 B A (A) 1 3 (B) 1 3 (C) 3 (D) 3

(43) Here is a velocity - time graph of a motorbike moving in one direction. Calculate the distance covered by it in last two seconds.

o V t 1 2 3 4 5 C 10m 5 (A) 5 m (B) 20 m (C) 50 m (D) 25 m (44) a t

In the above figure acceleration (a)  time (t) graph is given. Hence V ...

(A) a (B) _a (C) a2 _{(D) a}3 (45) t X o A B

The graph of displacent (x)  time (t) for an object is given in the figure. In which part of the graph the acceleration of the particle is positive ?

(A) OA (B) AB

(46) In a uniformly accelerated motion the slope of velocity - time graph gives .... (A) The instantaneous velocity (B) The acceleration

(C) The initial velocity (D) The final velocity

(47) The area covered by the curve of V – t graph and time axis is equal to magnitude of .... (A) change in velocity (B) change in acceleration

(C) displacement (D) final velocity

(48) An object moves in a straight line. It starts from the rest and its acceleration is 2ms–2_{. After reaching a}

cer-tain point it comes back to the original point. In this movement its acceleration is -3ms-2_{. till it comes to rest.}

The total time taken for the movement is 5 second. Calculate the maximum velocity. (A) 6 ms–1 _{(B) 5 ms}–1 _{(C) 10 ms}–1 _{(D) 4 ms}–1

(49) The relation between time and displacement of a moving particle is given by 2

t 2 x where  is a constant. The shape of the graph xy is ...

(A) parabola (B) hyperbola (C) ellips (D) circle (50) Here are the graphs of x of a moving body. Which of them is not suitable ?t

(A) t x o (B) t x o (C) t x (D) t x

(51) Here are the graphs of v of a moving body. Which of them is not suitable ?t

(A) t V (B) t V (C) t V (D) t V

Comprehension type questions

t

V

A

o

D

C

B

(52) Which area shows the displacement covered by the particle after time t (A) closed fig AODCA (B) closed fig. ABCA (C) closed fig. AODCBA (D) none of above (53) Which part shows initial velocity of the particle ?

(A) OA (B) AB (C) AC (D) AOA

(54) How will you calculate the acceleration of the particle ?

(A) taking length of AB (B) taking magnitude of BC (C) taking slope of AC (D) taking slope of AB (55)

o X

t

2 4 _{6 8}

Given graph shows relation between position and time. Find correct graph of acceleration  time (A) a t 2 4 _{6 8} (B) o a t 2 4 _{6 8} (C) o X t 2 4 _{6 8} (D) o X t 2 4 8 (56) t X 130 60 B A

Here are displacement  time graphs of particle A and B. If VV_A and V_B are velocities of the particles respectively, then A B V V = ... (A) 1 3 (B) 3 (C) 1 3 (D) 3

(57) X

t

2 4 6 8

Given graph shows relation between position (x)  time (t) Find the correct graph of velocity  time. (A) o V t 2 4 6 ₈ (B) V t 2 4 6 8 (C) V t 2 4 _{6 8} (D) V t 2 4 _{6 8}

(58) Particles A and B are released from the same height at an interval of 2 s. After some time t the distance between A and B is 100m. Calculate time t.

(A) 8 s (B) 6 s (C) 3 s (D) 12 s

(59) As shown in the figure a particle is released from P. It reachet at point Q at time t₁ and reaches at point R at time t₂ so 1

2 t t = .... (A) 1 3 (B) 1 2 (C) 2 1 (D) 4 1

(60) A particle moves in stright line. Its position is given by x = 2 + 5t – 3t2_.

Find the ratio of intial velocity and initial acceleration. (A) 5 6  (B) –5 6 (C) 6 5 (D) 6 – 5

(61) A particle is moving in a circle of radius R with constant speed. It coveres an angle  in some time interval. Find displacement in this interval of time.

(A) 2R cos 2 

(B) _2Rsinθ

2 (C) 2Rcos (D) 2Rsin

(62) A particle is moving in a straight line with initial velocity of 200 ms–1 _{acceleration of the particle}

is given by a = 3t2 _{– 2t. Find velocity of the particle at 10 second.}

(63) Angle of projection, maximum height and time to reach the maximum height of a particle are  , H and tm respectivley. Find the true relation.

(A) m H t 2g  (B) m 2H t = g (C) m 4H t = g (D) m H t = 4g

(64) Particle A is projected vertically upward from a top of a tower. At the same time particle B is dropped from the same point. The graph of distance (s) between the two particle varies with time is.

(A) t S (B) t S (C) t S (D) t S

(65) A car is moving with speed 30m. Due to application of brakes it travells 30m before stopping. Find its acceleration.

(A) 15m₂ s (B) 2 m –15 s (C) 2 m 30 s (D) 2 m 10 s

(66) A particle moves with a constant acceleration 2m/s2_{. Its intial velocity is 10m/s. Find velocity after t second.}

(A) (10 + t) ms–1 _{(B) 5(2 + t)ms}–1 _{(C) 2 (5 + t)ms}–1 _{(D) (10 + t}2_{) ms}–1

(67) A particle moves in a straight lime with constant acceleration. At t = 10s velocity and displacement of the particle are 16ms–1 _{and 39m respectively. What will be the velocity after 10 s ...}

(A) 22 ms–1 _{(B) 18 ms}–1 _{(C) 20 ms}–1 _{(D) 28 ms}–1

(68) A particle moves with constant acceleration 2m/s2 _{in x direction. The distance travelled in fifth}

second is 19 m. Calculate the distance travelled after 5 second.

(A) 50 m (B) 75 m (C) 80 m (D) 70 m

(69) Two bodies of masses m₁ and m₂ are dropped from heights H and 2H respectively. The ratio of time taken by the bodies to touch the ground is ...

(A) 1 2 (B) 2 (C) 1 2 (D) 2 1

(70) A freely falling stone crashes through a horizontal glass plate at time t and losses half of its velocity. Af-ter time t

2 it falls on the ground. The glass plate is 60 m high from the ground. Find the total distance travelled

by the stone. [g = 10ms–2_]

(A) 120 m (B) 80 m (C) 100 m (D) 140 m

(71) A freely falling object travells distance H. Its velocity is V. Hence, in travelling further distance of 4H its velocity will become ....

(A) 3V (B) 5V (C) 2V (D) 3V h 3h R Q P

(72) A ball is thrown vertically upward direction. Neglacting the air resistance velocity of the ball in air will

(A) zero (B) decrease when it is going up

(C) decrease when it is coming down (D) remain constant

(73) Two particles P and Q get 5 m closer each second while travelling in opposite direction. They get 1 m closer each second while travelling in same direction. The speeds of P and Q are respectively ...

(A) 5 ms–1_{, 1 ms}–1 _{(B) 3 ms}–1_{, 4 ms}–1 _{(C) 3 ms}–1_{, 2 ms}–1_{(D) 10 ms}–1_{, 5 ms}–1

(74) Motion of a porticle is described by an equation υ = A + y

_

_

distance and a constant respectively. Find the acceleratrion of the particle. (A) 1 unit (B) 2 unit (C) 1unit

2 (D) 3 unit

(75) The minumum distance in which a car can be stopped is x. The velocity of the car is V. If the velocity is 2V then find the stopping distance.

(A) 2x (B) 4x (C) 3x (D) 1 x

2

(76) A particle moves in one direction with acceleration 2 ms–2 _{and initial velocity 3 ms}–1_{.After what}

time its displacement will be 10 m ?

(A) 1 s (B) 2 s (C) 3 s (D) 4 s

(77) A goods train is moving with constant acceleration. when engine passes through a signal its speed is U. Midpoint of the train passes the signal with speed V. What will be the speed of the last wagon ? (A) 2 2 V – U 2 (B) 2 2 V U 2  (C) 2 2 2V U 2  (D) 2 2 2V – U

(78) Displacement of a particle in y direction is given by y = t2 _{– 5t + 5 where t is in second.}

Calculate the time when its velocity is zero.

(A) 5 s (B) 2.5 s (C) 10 s (D) 3 s (79) The area under acceleration versus time graph for any time interval represents...

(A) Intial velocity (B) final velocity (C) change invelocity in the time interval

(D) Distance covered by the particle

(80) A ball is thrown vertically upward. What is the velocity and acceleration of the ball at the maximum height ?

(A) –gt ms–1_{, 0 (B) 0, –9 ms}–2 _{(C) g ms}–1_{, 0 (D) 0, –gt ms}–2

(81) The relation between velocity and position of a particle is V = Ax + B where A and B are constants. Acceleration of the particle is 10 ms–2 _{when its velocity is V, How much is the acceleration when}

its velocity is 2V.

(82) A particle moves on a plane along the path y = Ax3 _{+ B in such a way that} dx

c

dt  . c, A,

B are constans. Calculate the acceleration of the particle. (A) ^ –2 3Axc jms (B) ^ 2 –2 5Axc jms (C) ^ 2 –2 3Axc jms (D) ^ ^ 2 –2 c i 3Axc j ms       

(83) The relation between velocity and position of a particle is given by V – x . Its initial velocity is zero. Find its velocity at time t 1

B  (A) e ms–1 _{(B) 0 ms}–1 _(C) 1 –1 ms e (D) e 2 _ms–1

(84) An object moves in x - y plane. Equations for displacement in x and y direction are x = 3sin2t and y = 3cos2t Speed of the particle is

(A) zero (B) constant and nonzero

(C) increasing with time t (D) decreasing with time t

(85) Motion of a particle is decribed by x = (t – 2)2 _{Find its velocity when it passes through origin.}

(A) 0 (B) 2 ms–1 _{(C) 4 ms}–1 _{(D) 8 ms}–1

(86) To introduce a vector quantity ....

(A) it needs magnitude not direction (B) it needs direction not magnitude

(C) it need both magnitude and direction (D) nothing is needed

(87) Which pair of two vectors is antiparallel. (A) _A B (B) _A B (C) A B (D) A B

(88) In the above figure _P and Q 

are two vectors. What from followings is true

P

Q

(A) _P and Q are equal (B) _P and Q are perpendicular (C) P and Q are antiparallel (D) _P and Q are in same direction (89) Which from the following is a scalar ?

(A) Electric current (B) Velocity (C) acceleration (D) Electric field (90) P and Q are equal vectors what from the followings is true.

(A) P and Q are antiparallel (B) P and Q are parallel