33



      

PHYSICS (2020-1988)

Includes 2020 Covid Re-NEET Solved Paper Aligned as per Class 11 and 12 NCERT Books

ALTIS VORTEX

33 NEET Years

CHAPTER-WISE SOLUTIONS with NCERT References

PHYSICS

Altis Vortex Delhi

EDITION : 2021 ISBN : 978-93-87902-38-1 BOOK CODE : 1144 Price : Rs. 300/-

Published By:

Altis Vortex

(Books & Publications) C-146, Gautam Nagar, Green Park New Delhi - 110049 Ph. No. - 011-26567270 Email : [email protected] Website : www.aim4aiims.in Rights All rights will be reserved by Publisher. No part of this book may be used or reproduced in any manner whatsoever without the written permission from author or publisher. Disclaimer : Every effort has been taken in compiling/editing of the concerned data/ information given in this book in various section, Also the questions in book contain are memory based so it is possible to remain some mistake due to human error if so kindly compare the data with the government publication, journals and notification.

Contents Class XI 1.

Units & Measurements

1

2.

Motion in a Straight Line

9

3.

Motion in a Plane

20

4.

Laws of Motion

31

5.

Work, Energy and Power

47

6.

System of Particles and Rotational Motion

64

7.

Gravitation

84

8.

Mechanical Properties of Solids

97

9.

Mechanical Properties of Fluids

99

10.

Thermal Properties of Matter

104

11.

Thermodynamics

113

12.

Kinetic Theory

126

13.

Oscillations

130

14.

Waves

143

Class XII 1.

Electric Charges and Fields

1

2.

Electrostatic Potential and Capacitance

8

3.

Current Electricity

21

4.

Moving Charges and Magnetism

44

5.

Magnetism and Matter

61

6.

Electromagnetic Induction

66

7.

Alternating Current

74

8.

Electromagnetic Waves

83

9.

Ray Optics and Optical Instruments

88

10.

Wave Optics

104

11.

Dual Nature of Radiation and Matter

111

12.

Atoms

125

13.

Nuclei

135

14.

Semiconductor Electronics

148

2020 NEET Solved Paper

168

2020 Covid Re-NEET Solved Paper

176

Syllabus Physics - XI UNIT I: Physical World and Measurement Details:• Physics: Scope and excitement; nature of physical laws; Physics, technology and society. • Need for measurement: Units of measurement; systems of units; SI units, fundamental and derived units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in measurement; significant figures. • Dimensions of physical quantities, dimensional analysis and its applications. UNIT II: Kinematics Details:• Frame of reference, Motion in a straight line; Position-time graph, speed and velocity. Uniform and non-uniform motion, average speed and instantaneous velocity. Uniformly accelerated motion, velocity-time and position-time graphs, for uniformly accelerated motion (graphical treatment). • Elementary concepts of differentiation and integration for describing motion. Scalar and vector quantities: Position and displacement vectors, general vectors, general vectors and notation, equality of vectors, multiplication of vectors by a real number; addition and subtraction of vectors. Relative velocity. • Unit vectors. Resolution of a vector in a plane-rectangular components. • Scalar and Vector products of Vectors. Motion in a plane. Cases of uniform velocity and uniform accelerationprojectile motion. Uniform circular motion. UNIT III: Laws of Motion Details:• Intuitive concept of force. Inertia, Newton’s first law of motion; momentum and Newton’s second law of motion; impulse; Newton’s third law of motion. Law of conservation of linear momentum and its applications. • Equilibrium of concurrent forces. Static and Kinetic friction, laws of friction, rolling friction, lubrication. • Dynamics of uniform circular motion. Centripetal force, examples of circular motion (vehicle on level circular road, vehicle on banked road). UNIT IV: Work, Energy and Power Details:• Work done by a constant force and variable force; kinetic energy, work-energy theorem, power. • Notion of potential energy, potential energy of a spring, conservative forces; conservation of mechanical energy (kinetic and potential energies); nonconservative forces; motion in a vertical circle, elastic and inelastic collisions in one and two dimensions.

UNIT V: Motion of System of Particles and Rigid Body Details:• Centre of mass of a two-particle system, momentum conservation and centre of mass motion. Centre of mass of a rigid body; centre of mass of uniform rod. • Moment of a force,-torque, angular momentum, conservation of angular momentum with some examples. • Equilibrium of rigid bodies, rigid body rotation and equation of rotational motion, comparison of linear and rotational motions; moment of inertia, radius of gyration. Values of M.I. for simple geometrical objects (no derivation). Statement of parallel and perpendicular axes theorems and their applications. UNIT VI: Gravitation Details:• Kepler’s laws of planetary motion. The universal law of gravitation. Acceleration due to gravity and its variation with altitude and depth. • Gravitational potential energy; gravitational potential. Escape velocity, orbital velocity of a satellite. Geostationary satellites. UNIT VII: Properties of Bulk Matter Details:• Elastic behavior, Stress-strain relationship. Hooke’s law, Young’s modulus, bulk modulus, shear, modulus of rigidity, poisson’s ratio; elastic energy. • Viscosity, Stokes’ law, terminal velocity, Reynold’s number, streamline and turbulent flow. Critical velocity, Bernoulli’s theorem and its applications. • Surface energy and surface tension, angle of contact, excess of pressure, application of surface tension ideas to drops, bubbles and capillary rise. • Heat, temperature, thermal expansion; thermal expansion of solids, liquids, and gases. Anomalous expansion. Specific heat capacity: Cp, Cv- calorimetry; change of state – latent heat. • Heat transfer- conduction and thermal conductivity, convection and radiation. Qualitative ideas of Black Body Radiation, Wein’s displacement law, and Green House effect. • Newton’s law of cooling and Stefan’s law. UNIT VIII: Thermodynamics Details:• Thermal equilibrium and definition of temperature (zeroth law of Thermodynamics). Heat, work and internal energy. First law of thermodynamics. Isothermal and adiabatic processes. • Second law of the thermodynamics: Reversible and irreversible processes. Heat engines and refrigerators. UNIT IX: Behaviour of Perfect Gas and Kinetic Theory Details:• Equation of state of a perfect gas, work done on compressing a gas. • Kinetic theory of gases: Assumptions, concept of pressure. Kinetic energy and temperature; degrees of freedom, law of equipartition of energy (statement only) and application to specific heat capacities of gases; concept of mean free path.

UNIT X: Oscillations and Waves Details:• Periodic motion-period, frequency, displacement as a function of time. Periodic functions. Simple harmonic motion(SHM) and its equation; phase; oscillations of a spring-restoring force and force constant; energy in SHM –Kinetic and potential energies; simple pendulum-derivation of expression for its time period; free, forced and damped oscillations (qualitative ideas only), resonance. • Wave motion. Longitudinal and transverse waves, speed of wave motion. Displacement relation for a progressive wave. Principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics. Beats. Doppler effect.

Physics - XII UNIT I: Electrostatics Details:• Electric charges and their conservation. Coulomb’s law-force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. • Electric field, electric field due to a point charge, electric field lines; electric dipole, electric field due to a dipole; torque on a dipole in a uniform electric field. • Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside) • Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges: equipotential surfaces, electrical potential energy of a system of two point charges and of electric diploes in an electrostatic field. • Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarization, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor, Van de Graaff generator. UNIT II: Current Electricity Details:• Electric current, flow of electric charges in a metallic conductor, drift velocity and mobility, and their relation with electric current; Ohm’s law, electrical resistance, V-I characteristics (liner and non-linear), electrical energy and power, electrical resistivity and conductivity. • Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance. • Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel. • Kirchhoff’s laws and simple applications. Wheatstone bridge, metre bridge. • Potentiometer-principle and applications to measure potential difference, and for comparing emf of two cells; measurement of internal resistance of a cell. UNIT III: Magnetic Effects of Current and Magnetism Details:• Concept of magnetic field, Oersted’s experiment. Biot-Savart law and its application to current carrying circular loop.

• Ampere’s law and its applications to infinitely long straight wire, straight and toroidal solenoids. Force on a moving charge in uniform magnetic and electric fields. Cyclotron. • Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel current-carrying conductors-definition of ampere. Torque experienced by a current loop in a magnetic field; moving coil galvanometerits current sensitivity and conversion to ammeter and voltmeter. • Current loop as a magnetic dipole and its magnetic dipole moment. Magnetic dipole moment of a revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements. • Para-, dia-and ferro-magnetic substances, with examples. • Electromagnetic and factors affecting their strengths. Permanent magnets. UNIT IV: Electromagnetic Induction and Alternating Currents Details:• Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents. Self and mutual inductance. • Alternating currents, peak and rms value of alternating current/ voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattles current. • AC generator and transformer. UNIT V: Electromagnetic Waves Details:• Need for displacement current. • Electromagnetic waves and their characteristics (qualitative ideas only). Transverse nature of electromagnetic waves. • Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays) including elementary facts about their uses. UNIT VI: Optics Details:• Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and its applications optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens-maker’s formula. Magnification, power of a lens, combination of thin lenses in contact combination of a lens and a mirror. Refraction and dispersion of light through a prism. • Scattering of light- blue colour of the sky and reddish appearance of the sun at sunrise and sunset. • Optical instruments: Human eye, image formation and accommodation, correction of eye defects (myopia and hypermetropia) using lenses. • Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers. • Wave optics: Wavefront and Huygens’ principle, reflection and refraction of plane wave at a plane surface using wavefronts. • Proof of laws of reflection and refraction using Huygens’ principle. • Interference, Young’s double hole experiment and expression for fringe width, coherent sources and sustained interference of light.

• Diffraction due to a single slit, width of central maximum. • Resolving power of microscopes and astronomical telescopes. Polarisation, plane polarized light; Brewster’s law, uses of plane polarized light and Polaroids. UNIT VII: Dual Nature of Matter and Radiation Details:• Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation- particle nature of light. • Matter waves- wave nature of particles, de Broglie relation. Davisson-Germer experiment (experimental details should be omitted; only conclusion should be explained). UNIT VIII: Atoms and Nuclei Details:• Alpha- particle scattering experiments; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum. Composition and size of nucleus, atomic masses, isotopes, isobars; isotones. • Radioactivity- alpha, beta and gamma particles/ rays and their properties decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number, nuclear fission and fusion. UNIT IX: Electronic Devices Details:• Energy bands in solids (qualitative ideas only), conductors, insulators and semiconductors; semiconductor diodeI-V characteristics in forward and reverse bias, diode as a rectifier; I-V characteristics of LED, photodiode, solar cell, and ner diode; Zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor; transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch .

CLASS XI

1

Units & Measurements

1. In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement of X, where X =

A 2B

1

2

1

C 3 D3

3 a   % b. 16%  13 

will be 

(2019)

c. – 10%

d. 10%

2. A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of –0.004 cm, the correct diameter of the ball is  (2018) a. 0.053 cm b. 0.525 cm c. 0.521 cm d. 0.529 cm 3. A physical quantity of the dimensions of length that can be formed out of c, G and

e2 is [c is velocity 4πε0

of light, G is universal constant of gravitation and e is charge]: (2017-Delhi)

 e2  a. c G   4πε0  2

c.

1

2



 b. 1  2

e2   c  G4πε0 

1

1 e d. 1 e  G G  2 c 4πε0 c 2  4πε0  2

2

2

1

2

4. A student performs an experiment of measuring the thickness of a slab with a vernier calliper whose 50 divisions of the main scale. He noted that zero of the vernier scale is between 7.00 cm and 7.05 cm mark of the main scale and 23rd division of the vernier scale exactly coincides with the main scale. The measured value of the thickness of the given slab using the calliper will be: (2017-Gujarat) a. 7.73 cm b. 7.23 cm c. 7.023 cm d. 7.073 cm

5. Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?  (2016 - II)

Gc a. hc b. h 3/ 2 G

hG c. hG d. 3/ 2 c5/ 2 c

6. If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be: (2015) a. [EV–1T–2] c. [E–2V–1T–3]

b. [EV–2T–2] d. [EV–2T–1]

7. If dimension of critical velocity of liquid flowing through a tube are expressed as νc∝[ηxρyrz] where η, ρ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by:  (2015 - Re) a. 1, 1, 1 b. 1, –1, –1 c. –1, –1, 1 d. –1, –1, –1 8. If Force (F) , Velocity (V) and Time (T) are taken as fundamental units, then the dimensions of mass are: (2014) a. [F V T–1] b. [F V T–2] -1 –1 c. [F V T ] d. [F V–1T] 9. In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows a 3b 2 . % error in P is:  (2013) P= cd a. 4%

b. 14%

c. 10%

d. 7%

10. The dimensions of (µ0ε0) are: (2012 Mains) a. [L1/2T-1/2] b. [L–1T] c. [LT–1] d. [L1/2T1/2] –1/2

11. The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are: (2012 Pre) a. kgms–1 b. kg/ms c. kgs–1 d. kgs

2

NEET 33 Years

12. The density of a material in CGS system of units is 4 g/cm3. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be: (2011 Mains) a. 0.4

b. 40

c. 400

d. 0.04

13. A student measures the distance traversed in free fall of a body, initially at rest in a given time. He used this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is: (2010 Mains) a. e2 – e1 b. e1 + 2e2 c. e1 + e2 d. e1 – 2e2 14. The dimension of

1 εo E 2 , where ε0 is permittivity 2

of free space and E is electric field, is: (2010 Pre) a. MLT–1

b. ML2T–2

c. ML–1T–2 d. ML2T–1

15. If the dimensions of a physical quantity are given by MaLbTc, then the physical quantity will be: (2009) a. Velocity if a = 1, b = 0, c = –1 b. Acceleration if a = 1, b = 1, c = –2 c. Force if a = 0, b = –1, c = –2 d. Pressure if a = 1, b = –1, c = –2 16. If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be: (2008) a. 2%

b. 4%

c. 6%

d. 8%

17. Which two of the following five physical parameters have the same dimensions? (2008) (a) Energy density (b) Refractive index (c) Dielectric constant (d) Young’s modulus (e) Magnetic field a. (a) and (e) b. (b) and (d) c. (c) and (e) d. (a) and (d) 18. Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be (2007) a. [ML2T-2] b. [ML2T-1I-1] c. [ML2T-3I-2] d. [ML2T-3I-1] 19. The velocity v of a particle at time t is given by

b , where a, b and c are constants. The t +c dimensions of a, b and c are respectively: (2006) a. [LT–2 ], [L] and [T] b. [L], [T] and [LT2] c. [L2T2], [LT] and [L] d. [L], [LT] and [T2] v = at +

20. The ratio of the dimensions of Planck’s constant and that of the moment of inertia is the dimension of:  (2005) a. Frequency b. Velocity c. Angular momentum d. Time 21. The dimensions of universal gravitational constant are:(2004) a. ML2T–1 b. M–2L3T–2 –2 2 –1 c. M L T d. M–1L3T–2 22. The dimension of Planck constant equals to that of: (2001) a. Energy b. Momentum c. Angular momentum d. Power 23. Which pair have not equal dimensions? (2000) a. Energy and torque b. Force and impulse c. Angular momentum and Planck’s constant d. Elastic modulus and pressure 24. The error in measurement of radius of a sphere is 0.1% then error in its volume is:  (1999) a. 0.3% b. 0.4% c. 0.5% d. 0.6% a  θ  b 25. An equation is given here  P + V 2  = V where   P = Pressure, V = Volume and θ = Absolute temperature. If a and b are constants, the dimensions of a will be: (1996) a. [ML–5 T–1] b. [ML5 T1] c. [ML5 T–2] d. [M–1L5T2] 26. The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and lengths are 3% and 2% respectively, the maximum error in the measurement of density would be: (1996) a. 12% b. 14% c. 7% d. 9% 27. The dimensions of impulse are equal to that of: (1996) a. Pressure b. Linear momentum c. Force d. Angular momentum 28. Which of the following dimensions will be the same as that of time? (1996) a.

L C b. R L

c. LC

d.

R L

29. Which of the following is a dimensional constant? (1995) a. Relative density b. Gravitational constant c. Refractive index d. Poisson ratio

3

Units & Measurements 30. The dimensions of RC is: (1995) a. Square of time b. Square of inverse time c. Time d. Inverse time. 31. Percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring mass and speed will be:(1995) a. 8%

b. 2%

c. 12%

d. 10%

38. The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by a relation f = amxky, where a is a dimensionless constant. The values of x and y are: (1990)

1 1 1 1 b. x= − ,y = − = ,y 2 2 2 2 1 1 1 1 c. x = , y = − d. x= − ,y = 2 2 2 2

a. = x

32. Which of the following has the dimensions of pressure? (1994, 90) a. [MLT–2] b. [ML–1 T–2] c. [ML–2 T–2] d. [M–1 L–1]

39. According to Newton, the viscous force acting between liquid layers of area A and velocity

33. Turpentine oil is flowing through a tube of length l and radius r. The pressure difference between the– two ends of the tube is P. The viscosity of oil is given

η is constant called coefficient of viscosity. The dimensional formula of η is:  (1990)

P(r 2 − x 2 ) by η = where v is the velocity of oil at a 4vl distance x from the axis of the tube. The dimensions of η are: (1993) a. [M0L0T0] b. [MLT–1] c. [ML2T–2] d. [ML–1T–1]

34. The time dependence of a physical quantity p is given by p = p0 exp (– αt2), where α is constant and t is the time. The constant α: (1993) a. Is dimensionless b. Has dimensions [T–2] c. Has dimensions [T2] d. Has dimensions of p 35. P represents radiation pressure, c represents speed of light and S represents radiation energy striking per unit area per sec. The non-zero integers x, y, z such that Px Sy cz is dimensionless are: (1992) a. x = 1, y = 1, z = 1 b. x = – 1, y = 1, z = 1 c. x = 1, y = –1, z = 1 d. x =1, y – 1, z = – 1 36. A certain body weighs 22.42 g and has a measured volume of 4.7 cc. The possible, error in the measurement of mass and volume are 0.01 g and 0.1 cc. Then maximum error in the density will be: (1991) a. 22% b. 2% c. 0.2% d. 0.02% 37. The dimensional formula of permeability of free space μ0 is (1991) a. [MLT–2 A–2] b. [M0 L–1 T] c. [M0 L T–1 A2] d. None of these

gradient Δv/ΔZ is given by F = −ηA

a. [ML–2 T–2] c. [ML2T2]

∆v , where ∆Z

b. [M0L0T0] d. [ML–1T–1]

40. If x = at + bt2, where x is the distance travelled by the body in kilometres while t is the time in seconds, then the units of b is: (1989) a. km/s

b. kms

c. km/s2

d. kms2

41. Of the following quantities, which one has dimensions different from the remaining three? (1989) a. Energy per unit volume b. Force per unit area c. Product of voltage and charge per unit volume d. Angular momentum. 42. Dimensional formula of self inductance is: (1989) a. [MLT–2 A–2] b. [ML2 T–1 A–2] c. [ML2T–2 A–2] d. [ML2 T2 A–1] 43. The dimensional formula of torque is: a. [ML2T–2] b. [MLT–2] c. [ML–1T–2] d. [ML–2 T–2]

(1989)

44. If C and R denote capacitance and resistance, the dimensional formula of CR is: (1988) 0 0 1 a. [M L T ] b. [M0L0T0] c. [M0L0T–1] d. Not expressible in terms of MLT 45. The dimensional formula of angular momentum is: (1988) a. [ML2T–2] b. [ML–2T–1] c. [MLT–1] d. [ML2T–1]

4

NEET 33 Years

Answer Key 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

b

d

d

c

c

b

b

d

b

c

c

b

b

c

d

c

d

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

b

c

a

b

d

b

c

a

a

d

c

b

a

c

d

b

a

35

36

37

38

39

40

41

42

43

44

45

c

b

a

d

d

c

d

c

a

a

d

Explanations 4. (c) NCERT (XI) Ch - 2, Pg. 24

1. (b) NCERT (XI) Ch - 2, Pg. 27 X=

1 A 2B 2

Least count = 1MSD – 1VSD

1

C 3 D3 ∆X ∆A 1 ∆B 1 ∆C × 100 = 2 × 100 + × 100 + × %error, X A 2 B 3 C ∆D 100 + 3 × 100 D = 2% + 1% + 1% + 12% = 16% 2. (d) NCERT (XI) Ch - 2, Pg. 24 Reading = MSR + (n × LC) + zero error = 0.5 + (25 × 0.001) + 0.004 3. (d) NCERT (XI) Ch - 2, Pg. 214 APPENDIX A9 c

–1

3

–2 b

3

–2 c

=L T M a + 3b + 3c = 1; – a –2b –2c = 0; – b + c = 0 a + 3b + 3c

–a –2b –2c

1 2



b=



a = –2

c=

 e2  L=c G 2   4πε0  −2

1

1/ 2

L=

1  e2  G  c 2  4πε0 

1

Thickness = 7 + 23 × 10–3 = 7.023 cm 5. (c) NCERT (XI) Ch - 2, Pg. 31

 ∝ h x G ycz M 0 L1T 0 = ( ML2T −1 ) ( M −1L3T −2 ) ( LT −1 ) x

= M x − y L2x + 3y + z T − x − 2y − z Equating: 1 1 3 −  ⇒ x = ; y = ;z = 2 2 2  2x + 3y + z = 1 hG − x − 2y − z = 0  ⇒  ∝ 3 c 2

–b +c

1 2

↓

S.T ∝ [E]a [V]b [T]c ∝ [ML2T–2]a [LT–1]b [T]c MT–2 ∝ Ma L2a+b T–2a-b+c On comparing both sides 2a + b = 0 , –2a – b + c = –2

2

y

6. (b) NCERT (XI) Ch - 2, Pg. 32-33

= [LT ] [M L T ] [ML T ] –1 a

49 × 5 × 10−2 50

x−y= 0

= 0.529 cm

2  a b  e L = [c] [G ]    4πε 0 

= 5 × 10−2 −

a = 1, b = –2, c = –2 we get ST = EV–2 T–2

z

5

Units & Measurements 7. (b) NCERT (XI) Ch - 2, Pg. 32-33

=

ν c ∝ η ρ r  x

y z

x

y

 L1T −1  ∝  M1L−1T −1   M1L−3   L1   L1T −1  ∝  M x + y   L− x − 3y + z  T − x 

z

Taking comparison on both size x + y = 0, –x – 3y + z = 1, –x = –1 x = 1, y = –1, z = –1 8. (d) NCERT (XI) Ch - 2, Pg. 32-33

  Force Force = [ Mass] =    Acceleration   Velocity/time  =  FV −1T  9. (b) NCERT (XI) Ch - 2, Pg. 26-27

a 3b 2 ∆P ∆b ∆c ∆d   ∆a P= ⇒ = ±3 +2 + +  cd P b c d   a =± ( 3 × 1 + 2 × 2 + 3 + 4 ) ⇒ ±14% 10. (c) NCERT (XI) Ch - 2, Pg. 32-33

= c Speed of light,

1 =  LT −1  µ 0ε 0

11. (c) NCERT (XI) Ch - 2, Pg. 32-33 Let F = kv

 MLT −2  F = [ k ] =  −1=  MT −1   v   LT  Hence units of k is kgs–1 12. (b) ∴ n1u1 = n 2u 2

g 100 g 4 3 = n2 3 cm (10 cm ) 40 ⇒ n2 = 13. (b) NCERT (XI) Ch - 2, Pg. 26

1 2 2h gt ⇒ = g 2 t2 ∆g ∆t   ∆h × 100 = + 2  × 100 =e1 + 2e 2 So, g t   h

= h

14. (c) NCERT (XI) Ch - 2, Pg. 32-33 1 2  2 ε0 E  = Energy density  

ML2T −2 ML−1T −2 = L3

15. (d) NCERT (XI) Ch - 2, Pg. 32 [Force] = MLT –2 [Pressure] = ML–1T –2 [Velocity] = M0LT –1 [Acceleration] = M0LT –2 16. (c) NCERT (XI) Ch - 2, Pg. 26-27

4 3 πr 3

Volume of sphere=

∆= r 2% ⇒ ⇒

∆v 3∆r = V r

∆v = 3 × 2 = 6% V

Error in determination of volume of sphere is equal to 6%. 2 −2  Energy  ML T 17. (d) (a) Energy= density =  L3  Volume 

Energy density = [ML–1T–2] (b) [Refractive index] = M0L0T0 (c) [Dielectric constant] = M0L0T0  Stress  −1 −2 = = (d) Young’s modulus  ML T  Strain  F (e) Magnetic field = ( B ) = ML0T −2A −1  qv  So, [(a) and (d)] and [(b) and (c)] have same dimension 18. (c) According to Ohm’s law, V = RI or R =

V I

V Dimensions of =

2 −2 W  ML T  = q [ IT ]

 ML2T −2 / IT  = ∴ [R ]  =  ML2T −3I −2  [ I]

b t+c As we know that only similar quantities can be added or subtracted so [c] = T

19. (a) v= at +

   

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