The secret of

KOTA

now at your Doorstep

PHYSICS 60 + 29

DPP BOOKLET

Topic-wise

Chapter-wise Tests for Concept Checking & Speed Building

Ü Collection of 2700 + MCQ’s of all variety of questions Ü Unique & innovative way of learning Ü Detailed solutions to Topic-wise & Chapter-wise practice sheets Ü Covers all important concepts of each topic Ü As per latest pattern & syllabus

Improves your learning by at least

20%

•

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Daily Practice Problem (DPP) Sheets PHYSICS for JEE-Main (Kota's formula to Success) PREPARE

ASSESS

IMPROVE

Assessment is the most integral part of a student’s preparation but still most of them avoid it. Only assessment can tell where you stand and how you can improve from that point. So it is very important that you take the right assessment, which is on the correct pattern, has the same level of difficulty as the actual exam and covers all the important concepts of the subject. Disha Publication launches a first of its kind product which changed the way coaching was conducted in KOTA - the hub of Engineering and Medical Entrance education in India. The book “Daily Practice Problem (DPP) Sheets for JEE Main” is precise, apt and tuned to all the requirements of a JEE Main aspirant. KEY DIFFERENTIATING FEATURES OF THE DPP SHEETS •

Part A provides 60 DPP's with division of the complete JEE Main syllabus of physics into 60 most important Topics. Each of the chapter has been broken into 2 or more topics.

•

Part B consist of — Chapter-wise tests based on NCERT and JEE Main syllabus.

•

Time Limit, Maximum Marks, Cut-off, Qualifying Scores have been provided for each DPP Sheet/ topic. You must attempt each Sheet in test like conditions following the time limits. The Cut-off for each Sheet indicate that students must at least score this much whereas if a student scores more or equal to Qualifying Score it means his/ her preparation is good in that topic or chapter. Further to achieve perfect preparation in a topic or chapter one has to score atleast 80 marks

•

Ultimate tool for Concept Checking & Speed Building.

•

Collection of 2700 + Standardised MCQ’s of all variety of NEW pattern questions – MCQs with only one correct option and Assertion-Reason.

•

Unique & innovative way of learning. Whenever you have prepared a topic (Part A) or a chapter (Part B) just attempt that worksheet.

•

Do not refer the solutions until and unless you have made all the efforts to solve the DPP Sheets.

•

Covers all important Concepts of each Topic in the form of different Questions in the DPP Sheets.

•

As per latest pattern & syllabus of JEE Main exam.

•

Compliant to all boards of education.

No matter where you PREPARE from – a coaching or NCERT books or any other textbook/ Guide - Daily Practice Problem Sheets provides you the right ASSESSMENT on each topic and chapter. Your performance provides you the right clues to IMPROVE your concepts so as to perform better in the final examination. It is to be noted here that these are not tests but act as a checklist of student’s learning and ability to apply concepts to different problems. Do proper analysis after you attempt each DPP sheet and try to locate your weak areas. It is our strong belief that if an aspirant works hard on the clues provided through each of the DPP sheets he/ she can improve his/ her learning and finally the SCORE by at least 20%.

Χisha ∆xperts

The book comprises of following two parts Part A : Topic-wise DPP Sheets Page No. Detailed Index (i) to (iv) Topic-wise Sheets 1-60(each sheet 4 pages) p1 - p-4 Solutions of Topic-wise Sheets 1 - 158 Part B : Chapter-wise DPP Sheets Detailed Index Chapter-wise Sheets 1-29 Solutions of Chapter-wise Sheets

(a) & (b) p-1 – p-116 S-1– S-96

TOPIC-WISE DPP SHEETS WITH SOLUTIONS

[i]

INDEX/SYLLABUS DPP-1

Page No.

DPP-1

PHYSICAL WORLD, UNITS & DIMENSIONS

P1 - P 4

DPP-2

MEASUREMENTS (ERRORS)

P1 - P 4

DPP-3

MOTION IN A STRAIGHT LINE 1 (Distance, Displacement, Uniform & Non-uniform motion)

P1 - P 4

DPP-4

MOTION IN A STRAIGHT LINE 2 (Relative Motion & Motion Under Gravity)

P1 - P 4

DPP-5

VECTORS

P1 - P 4

DPP-6

MOTION IN A PLANE-1 (Projectile Motion)

P1 - P 4

DPP-7

MOTION IN A PLANE-2 (Horizontal Circular Motion)

P1 - P 4

DPP-8

MOTION IN A PLANE-3 (Vertical Circular Motion, Relative Motion)

P1 - P 4

DPP-9

LAWS OF MOTION-1 (Newton's laws, momentum, pseudo force concept)

P1 - P 4

DPP-10

LAWS OF MOTION-2 (Blocks in contact, connected by string, pulley arrangement)

P1 - P 4

DPP-11

LAWS OF MOTION-3 (Friction)

P1 - P 4

DPP-12

WORK, ENERGY AND POWER-1 (Work by constant and variable forces, kinetic and potential energy, work energy theorem) P1 - P 4

DPP-13

WORK, ENERGY AND POWER-2 (Conservation of momentum and energy, collision, rocket case)

P1 - P 4

DPP-14

CENTRE OF MASS AND ITS MOTION

P1 - P 4

DPP-15

ROTATIONAL MOTION – 1: Basic concepts of rotational motion, moment of a force, torque, angular momentum and its conservation with application

P1 - P 4

DPP-16

ROTATIONAL MOTION-2 : Moment of inertia, radius of gyration, (values of moments of inertia simple geometrical objects) P1 - P 4

DPP-17

ROTATIONAL MOTION - 3 : Rolling Motion, Parallel and perpendicular theorems and their applications, Rigid body rotation, equations of rotational motion

P1 - P 4

DPP-18

GRAVITATION - 1 (The Universal law of gravitation, Acceleration due to gravity and its variation with altitude and depth, Kepler's law of planetary motion) P1 - P 4

DPP-19

GRAVITATION - 2 (Gravitational potential energy, Gravitational potential, Escape velocity & Orbital velocity of a satellite, Geo-stationary satellites) P1 - P 4

DPP-20

MECHANICAL PROPERTIES OF SOLIDS

P1 - P 4

DPP-21

FLUID MECHANICS

P1 - P 4

DPP-22

THERMAL EXPANSION, CALORIMETRY AND CHANGE OF STATE

P1 - P 4

DPP-23

HEAT TRANSFER & NEWTON’S LAW OF COOLING

P1 - P 4

DPP-24

THERMODYNAMICS-1 (Thermal equilibrium, zeroth law of thermodynamics, concept of temperature, Heat, work and internal energy, Different thermodynamic processes) P1 - P 4

DPP-25

THERMODYNAMICS-2 (1st and 2nd laws of thermodynamics, Reversible & irreversible processes, Carnot engine and its efficiency) P1 - P 4

DPP-26

KINETIC THEORY

P1 - P 4

[ii]

DPP-27

OSCILLATIONS-1 (Periodic motion - period, Frequency, Displacement as a function of time. Periodic functions, Simple harmonic motion and its equation, Energy in S.H.M. - kinetic and potential energies) P1 - P 4

DPP-28

OSCILLATIONS-2 (Oscillations of a spring, simple pendulum, free, forced and damped oscillations, Resonance) P1 - P 4

DPP-29

WAVES-1 (Wave motion, longitudinal and transverse waves, speed of a wave, displacement relation for a progressive wave, principle of superposition of waves, reflection of waves) P1 - P 4

DPP-30

WAVES-2 (Standing waves in strings and organ pipes, Fundamental mode and harmonics, Beats, Doppler effect in sound) P1 - P 4

DPP-31

PRACTICAL PHYSICS - 1

P1 - P 4

DPP-32

ELECTROSTATICS-1 (Coulomb's law, electric field, field lines, Gauss's law)

P1 - P 4

DPP-33

ELECTROSTATICS-2 (Electric potential and potential difference, equipotential surfaces, electric dipole) P1 - P 4

DPP-34

ELECTROSTATICS -3 (Electrostatic Potential energy, conductors)

P1 - P 4

DPP-35

ELECTROSTATICS-4 (Capacitors, dielectrics)

P1 - P 4

DPP-36

CURRENT ELECTRICITY – 1 (Electric Current, drift velocity, Ohm's law, Electrical resistance, Resistances of different materials, V-I characteristics of Ohm and non-ohmic conductors, electrical energy and power, Electrical resistivity, Colour code of resistors, Temperature dependance of resistance) P1 - P 4

DPP-37

CURRENT ELECTRICITY – 2 Electrical cell and its internal resistance, Potential difference and E.M.F of a cell, Combination of cells in series and in parallel, Kirchoff's laws and their applications, RC transient circuit, Galvanometer, Ammeter, Voltmeter] P1 - P 4

DPP-38

CURRENT ELECTRICITY-3 : Wheatstone bridge, Meter bridge, Potentiometer-principle and its applications. P1 - P 4

DPP-39

MAGNETIC EFFECTS OF CURRENT-1 (Magnetic field due to current carrying wires, Biot savart law) P1 - P 4

DPP-40

MAGNETIC EFFECTS OF CURRENT-2 : (Motion of charge particle in a magnetic field, force between current carrying wires.) P1 - P 4

DPP-41

MAGNETIC EFFECTS OF CURRENT-3 (Magnetic dipole, Current carrying loop in magnetic field,Galvanometer )

P1 - P 4

DPP-42

MAGNETISM AND MATTER - 1 (Bar magnet as an equivalent solenoid, Magnetic field lines, Earth's magnetic field and magnetic elements) P1 - P 4

DPP-43

MAGNETISM & MATTER-2 (Para, dia and ferro-magnetic substances, magnetic susceptibility and permeability, Hysteresis, Electromagnets and permanent magnets.) P1 - P 4

DPP-44

ELECTROMAGNETIC INDUCTION-1 (Magnetic flux, Faraday's law of electromagnetic induction, Lenz's law, motional e.m.f.) P1 - P 4

DPP-45

ELECTROMAGNETIC INDUCTION - 2 : Self inductance, mutual inductance, Growth and decay of current in L.R. circuit, Transformer, Electric motor, Generator P1 - P 4

DPP-46

ALTERNATING CURRENT - 1 (Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance, Pure circuits, LR, CR ac circuits.) P1 - P 4

DPP-47

ALTERNATING CURRENT - 2 (LCR series circuit, resonance, quality factor, power in AC circuits, wattless and power current) P1 - P 4 [iii]

DPP-48

EM WAVES

P1 - P 4

DPP-49

RAY OPTICS-1 (Reflection on plane mirrors and curved mirrors)

P1 - P 4

DPP-50

RAY OPTICS - II (Refraction on plane surface, total internal reflection, prism)

P1 - P 4

DPP-51

RAY OPTICS - 3 (Refraction on curved surface lens, Optical instrument)

P1 - P 4

DPP-52

WAVE OPTICS - I (Interference of Light)

P1 - P 4

DPP-53

WAVE OPTICS - II (Diffraction and polarisation of light)

P1 - P 4

DPP-54

DUAL NATURE OF MATTER & RADIATION (Matter Waves, Photon, Photoelectric effect, X-ray)

P1 - P 4

DPP-55

ATOMS

P1 - P 4

DPP-56

NUCLEI

P1 - P 4

DPP-57

SEMICONDUCTOR ELECTRONICS - 1 (Semiconductors, LED, Photodiode, Zener diode)

P1 - P 4

DPP-58

SEMICONDUCTOR ELECTRONICS-2 (Junction transistor, transistor action, characteristics of a transistor, transistor as an amplifier, logic gates) P1 - P 4

DPP-59

COMMUNICATION SYSTEMS, LASER

P1 - P 4

DPP-60

PRACTICAL PHYSICS - 2

P1 - P 4

Solutions to Topic-wise DPP Sheets (1-60)

[iv]

1-158

DPP - Daily Practice Problems Name :

Date :

Start Time :

End Time :

01 SYLLABUS : Physical World, Units & Dimensions

Max. Marks : 120

Time : 60 min. GENERAL INSTRUCTIONS

• • • • •

The Daily Practice Problem Sheet contains 30 MCQ's. For each question only one option is correct. Darken the correct circle/ bubble in the Response Grid provided on each page. You have to evaluate your Response Grids yourself with the help of solution booklet. Each correct answer will get you 4 marks and 1 mark shall be deduced for each incorrect answer. No mark will be given/ deducted if no bubble is filled. Keep a timer in front of you and stop immediately at the end of 60 min. The sheet follows a particular syllabus. Do not attempt the sheet before you have completed your preparation for that syllabus. Refer syllabus sheet in the starting of the book for the syllabus of all the DPP sheets. After completing the sheet check your answers with the solution booklet and complete the Result Grid. Finally spend time to analyse your performance and revise the areas which emerge out as weak in your evaluation.

DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice questions. Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONE choice is correct. Q.1 If L, C and R represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency? (a) (c)

1 RC

1 LC

(b)

R L

(d)

C L

aZ

Q.2 Number of particles crossing unit area perpendicular to X-axis in unit time is given by n = - D

RESPONSE GRID

1.

and n2 are number of particles per unit volume in the position x1 and x2. Find dimensions of D called as diffusion constant. (a) [M 0 L T 2] (b) [M 0 L2 T –4] (c) [M 0 L T –3] (d) [M 0 L2 T –1] 2 Q.3 X = 3YZ find dimensions of Y in (MKSA) system, if X and Z are the dimensions of capacity and magnetic field respectively (a) [M –3L –2T – 4A –1] (b) [ML– 2] –3 –2 4 4 (c) [M L T A ] (d) [M –3L– 2T 8A 4]

n2 - n1 , where n1 x2 - x1

2.

a Q.4 In the relation P = e - k q , P is pressure, Z is the distance, b k is Boltzmann constant and q is the temperature. The dimensional formula of b will be (a) [M 0L 2T 0] (b) [M 1L 2T 1] 1 0 –1 (c) [M L T ] (d) [M 0L 2T –1]

3. Space for Rough Work

4.

DPP/ P 01

2 1/ 2

P éF ù Q.5 The frequency of vibration of string is given by n = ê ú 2l ë m û

.

Here P is number of segments in the string and l is the length. The dimensional formula for m will be (a) [M 0LT –1] (b) [ML 0T –1] –1 0 (c) [ML T ] (d) [M 0L 0T 0] Q.6 What is the relationship between dyne and newton of force? (a) 1 dyne = 10–5 newton (b) 1 dyne = 10–7 newton (c) 1 dyne = 105 newton (d) 1 dyne = 107 newton Q.7 The speed of light (c), gravitational constant (G) and Planck's constant (h) are taken as the fundamental units in a system. The dimensions of time in this new system should be (a) G1/2 h1/2 c –5/2 (b) G–1/2 h 1/2 c 1/2 1/2 1/2 –3/2 (c) G h c (d) G1/2 h 1/2 c 1/2 Q.8 If the constant of gravitation (G), Planck's constant (h) and the velocity of light (c) be chosen as fundamental units. The dimensions of the radius of gyration is (a) h1/2 c –3/2G 1/2 (b) h1/2 c 3/2 G 1/2 (c) h1/2 c –3/2 G –1/2 (d) h–1/2 c –3/2 G 1/2 Q.9 The magnitude of any physical quantity (a) depends on the method of measurement (b) does not depend on the method of measurement (c) is more in SI system than in CGS system (d) directly proportional to the fundamental units of mass, length and time Q.10 The unit of Stefan's constant s is (a) Wm–2 K–1 (b) Wm2K–4 (c) Wm–2 K–4 (d) Wm–2K4 2 Q.11 In S = a + bt + ct , S is measured in metres and t in seconds. The unit of c is (a) ms–2 (b) m (c) ms–1 (d) None

RESPONSE GRID

Q.12 Wavelength of ray of light is 0.00006 m. It is equal to (a) 6 microns (b) 60 microns (c) 600 microns (d) 0.6 microns Q.13 SI unit of permittivity is (a) C2 m2 N–2 (b) C–1 m 2N –2 2 2 2 (c) C m N (d) C2 m–2 N –1 1 e E2 (e0 = permittivity of free space 2 0 and E = electric field) are (a) MLT–1 (b) ML2 T–2 (c) ML–1 T–2 (d) ML2 T–1 Q.15 Which of the following pairs is wrong? (a) Pressure-Baromter (b) Relative density-Pyrometer (c) Temperature-Thermometer (d) Earthquake-Seismograph Q.16 A physical quantity x depends on quantities y and z as follows: x = Ay + B tan Cz, where A, B and C are constants. Which of the following do not have the same dimensions? (a) x and B (b) C and z–1 (c) y and B/A (d) x and A Q.17 If the time period (T) of vibration of a liquid drop depends on surface tension (S), radius (r) of the drop and density (r) of the liquid, then the expression of T is

Q.14 The dimensions of

(a) T = k rr 3 / S

(b) T = k r1/ 2 r 3 / S

(c) T = k rr 3 / S1/ 2

(d) None of these

Q.18 The dimensional formula for Planck’s constant (h) is (a) [ML–2T–3 ] (b) [M0L2T–2 ] 0 2 –1 (c) [M L T ] (d) [ML–2T–2 ] Q.19 What are the dimensions of permeability (m0) of vaccum? (a) MLT–2I2 (b) MLT–2I–2 –1 –2 2 (c) ML T I (d) ML–1T –2I–2

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

Space for Rough Work

DPP/ P 01

3

Q.20 A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity h. After some time the velocity of the ball attains a constant value known as terminal velocity vT. The terminal velocity depends on (i) the mass of the ball m, (ii) h, (iii) r and (iv) acceleration due to gravity g. Which of the following relations is dimensionally correct? hr (b) vT µ mg

mg hr

(a)

vT µ

(c)

vT µ hrmg

(d) vT µ

mgr h

Q.21 The equation of state of some gases can be expressed as æ a çP+ 2 V è

ö ÷ (V - b) = RT . Here P is the pressure, V is the ø

volume, T is the absolute temperature and a, b and R are constants. The dimensions of 'a' are (a) ML5 T–2 (b) ML–1 T–2 (c) M0L3T0

(d) M0L6T0

Q.23 P represents radiation pressure, c represents speed of light and S represents radiation energy striking unit area per sec. The non zero integers x, y, z such that Px Sy cz is dimensionless are (1) x = 1 (2) y = – 1 (3) z = 1 (4) x = – 1 Q.24 Which of the following pairs have same dimensions? (1) Angular momentum and work (2) Torque and work (3) Energy and Young’s modulus (4) Light year and wavelength DIRECTION (Q.25-Q.27) : Read the passage given below and answer the questions that follows : Three of the fundamental constants of physics are the universal gravitational constant, G = 6.7 × 10–11m3kg–1s–2, the speed of light, c = 3.0 × 10 8 m/s, and Planck’s constant, h = 6.6 × 10–34 kg m2 s–1. Q.25 Find a combination of these three constants that has the dimensions of time. This time is called the Planck time and represents the age of the universe before which the laws of physics as presently understood cannot be applied.

DIRECTIONS (Q.22-Q.24) : In the following questions, more than one of the answers given are correct. Select the correct answers and mark it according to the following codes:

(a)

Codes : (a)

1, 2 and 3 are correct

(b) 1 and 2 are correct

(c)

2 and 4 are correct

(d) 1 and 3 are correct

Q.22 The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by a relation of the type f = c mx ky, where c is a dimensionless constant. The values of x and y are 1 2

(1)

x=

(3)

y=-

RESPONSE GRID

1 2

(2)

x=-

(4)

y=

1 2

(c)

hG c

(b)

4

hG c

(d)

hG c3

hG c5

Q.26 Find the value of Planck time in seconds (a) 1.3 × 10– 33 s (b) 1.3 × 10– 43 s – 13 (c) 2.3 × 10 s (d) 0.3 × 10– 23 s Q.27 The energy of a photon is given by E = hc . l If l = 4 ´ 10 -7 m , the energy of photon is

1 2

20.

21.

22.

25.

26.

27.

(a) 3.0 eV

(b) 4.5 eV

(c) 2.10 eV

(d) 3.95 eV

Space for Rough Work

23.

24.

DPP/ P 01

4 DIRECTIONS (Q. 28-Q.30) : Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Each of these questions has four alternative choices, only one of which is the correct answer. You have to select the correct choice. (a) (b) (c) (d)

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1. Statement -1 is False, Statement-2 is True. Statement -1 is True, Statement-2 is False.

Q.28 Statement -1 : Unit of Rydberg constant R is m–1 Statement -2 : It follows from Bohr’s formula

RESPONSE GRID

28.

29.

æ 1 1 ö v = R ç - ÷ , where the symbols have their usual ç n2 n 2 ÷ è 1 2 ø

meaning. Q.29 Statement -1: The time period of a pendulum is given by the formula, T = 2p g / l . Statement -2: According to the principle of homogeneity of dimensions, only that formula is correct in which the dimensions of L.H.S. is equal to dimensions of R.H.S. Q.30 Statement -1: L/R and CR both have same dimensions. Statement -2: L/R and CR both have dimension of time.

30.

DAILY PRACTICE PROBLEM SHEET 1 - PHYSICS Total Questions 30 Total Marks Attempted Correct Incorrect Net Score Cut-off Score 30 Qualifying Score Success Gap = Net Score – Qualifying Score Net Score = (Correct × 4) – (Incorrect × 1)

Space for Rough Work

120

50

DPP - Daily Practice Problems Name :

Date : End Time :

Start Time :

02 SYLLABUS : Measurements (Errors)

Max. Marks : 120

Time : 60 min. GENERAL INSTRUCTIONS

• • • • •

The Daily Practice Problem Sheet contains 30 MCQ's. For each question only one option is correct. Darken the correct circle/ bubble in the Response Grid provided on each page. You have to evaluate your Response Grids yourself with the help of solution booklet. Each correct answer will get you 4 marks and 1 mark shall be deduced for each incorrect answer. No mark will be given/ deducted if no bubble is filled. Keep a timer in front of you and stop immediately at the end of 60 min. The sheet follows a particular syllabus. Do not attempt the sheet before you have completed your preparation for that syllabus. Refer syllabus sheet in the starting of the book for the syllabus of all the DPP sheets. After completing the sheet check your answers with the solution booklet and complete the Result Grid. Finally spend time to analyse your performance and revise the areas which emerge out as weak in your evaluation.

Q.1 A wire has a mass 0.3 ± 0.003g, radius 0.5 ± 0.005 mm and length 6 ± 0.06 cm. The maximum percentage error in the measurement of its density is (a) 1 (b) 2 (c) 3 (d) 4 Q.2 If 97.52 is divided by 2.54, the correct result in terms of significant figures is

measurement in a, b, c and d are 1%, 3%, 2% and 2% respectiely. What is the percentage error in the quantity A (a) 12% (b) 7% (c) 5% (d) 14% Q.4 A physical quantity is given by X = M a LbT c . The percentage error in measurement of M, L and T are a, b and g respectively. Then maximum percentage error in the quantity X is (a) aa+ bb + cg (b) aa+ bb – cg

(a) 38.4 (b) 38.3937 (c) 38.394 (d) 38.39 Q.3 A physical quantity A is related to four observable a, b, c and d as follows, A =

RESPONSE GRID

1.

a 2b3 c d

the percentage errors of

2.

(c)

3.

a b c + + a b g

(d) None of these

4.

DPP/ P 02

2 Q.5 If the length of rod A is 3.25 ± 0.01 cm and that of B is 4.19 ± 0.01 cm then the rod B is longer than rod A by (a) 0.94 ± 0.00 cm (b) 0.94 ± 0.01 cm (c) 0.94 ± 0.02 cm (d) 0.94 ± 0.005 cm Q.6 If L = 2.331 cm, B = 2.1 cm, then L + B = (a) 4.431 cm (b) 4.43 cm (c) 4.4 cm (d) 4 cm Q.7 The number of significant figures in all the given numbers 25.12, 2009, 4.156 and 1.217 × 10–4 is (a) 1 (b) 2 (c) 3 (d) 4 Q.8 In an experiment, the following observation's were recorded: L = 2.820 m, M = 3.00 kg, l = 0.087 cm, Diameter D = 0.041 cm. Taking g = 9.81 m/s2 using the formula, Y = 4 MgL , the maximum percentage error in Y pD 2l is (a) 7.96% (b) 4.56% (c) 6.50% (d) 8.42% Q.9 A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation a =

b a cb d g ed

Q.10 The period of oscillation of a simple pendulum is given by

l where l is about 100 cm and is known to have g 1mm accuracy. The period is about 2s. The time of 100 oscillations is measured by a stopwatch of least count 0.1s. The percentage error in g is (a) 0.1%

(b) 1%

(c) 0.2%

(d) 0.8%

RESPONSE GRID

Q.14 The resistance R =

.

If the maximum errors in the measurement of b, c, d and e are b1%, c1%, d1%, and e1%, then the maximum error in the value of a determined by the experiment is (a) (b1+ c1+ d1+ e1)% (b) (b1+ c1– d1– e1)% (c) (ab1+ bc1– gd1– de1)%(d) (ab1+ bc1+ gd1+ de1)%

T = 2p

Q.11 The mean time period of second's pendulum is 2.00s and mean absolute error in the time period is 0.05s. To express maximum estimate of error, the time period should be written as (a) (2.00 ± 0.01)s (b) (2.00 + 0.025) s (c) (2.00 ± 0.05) s (d) (2.00 ± 0.10) s Q.12 Error in the measurement of radius of a sphere is 1%. The error in the calculated value of its volume is (a) 1% (b) 3% (c) 5% (d) 7% Q.13 The relative density of material of a body is found by weighing it first in air and then in water. If the weight in air is (5.00 ± 0.05) newton and weight in water is (4.00 ± 0.05) newton. Then the relative density along with the maximum permissible percentage error is (a) 5.0 ± 11% (b) 5.0 ± 1% (c) 5.0 ± 6% (d) 1.25 ± 5% V where V = 100 ± 5 volts and i

i = 10 ± 0.2 amperes. What is the total error in R ? (a) 5%

(b) 7%

(c) 5.2%

(d)

5 % 2

Q.15 The length of a cylinder is measured with a meter rod having least count 0.1 cm. Its diameter is measured with vernier calipers having least count 0.01 cm. Given that length is 5.0 cm. and radius is 2.0 cm. The percentage error in the calculated value of the volume will be (a) 1% (b) 2% (c) 3% (d) 4% Q.16 According to Joule’s law of heating, heat produced H = I2Rt, where I is current, R is resistance and t is time . If the errors in the measurements of I,R. and t are 3%, 4% and 6% respectively then error in the measurement of H is (a) ± 17% (b) ± 16% (c) ± 19% (d) ± 25%

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6.

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Q.17 A physical quantity P is given by P =

1 3 2 A B 3 C -4 D 2

. The quantity

which brings in the maximum percentage error in P is (a) A (b) B (c) C (d) D Q.18 If there is a positive error of 50% in the measurement of velocity of a body, then the error in the measurement of kinetic energy is (a) 25% (b) 50% (c) 100% (d) 125% Q.19 The random error in the arithmetic mean of 100 observations is x; then random error in the arithmetic mean of 400 observations would be 1 1 x (a) 4x (b) x (c) 2x (d) 4 2 Q.20 The percentage errors in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed? (a) 11% (b) 8% (c) 5% (d) 1% Q.21 The unit of percentage error is (a) Same as that of physical quantity (b) Different from that of physical quantity (c) Percentage error is unitless (d) Errors have got their own units which are different from that of physical quantity measured DIRECTIONS (Q.22-Q.24) : In the following questions, more than one of the answers given are correct. Select the correct answers and mark it according to the following codes: Codes : (a) 1, 2 and 3 are correct (b) 1 and 2 are correct (c) 2 and 4 are correct (d) 1 and 3 are correct

RESPONSE GRID

Q.22 In the context of accuracy of measurement and significant figures in expressing results of experiment, which of the following is/are correct? 1. Out of the two measurements 50.14 cm and 0.00025 ampere, the first one has greater accuracy 2. Out of the two measurements 50.14 cm and 0.00025 ampere, the second has greater accuracy. 3. If one travels 478 km by rail and 397 m by road, the total distance travelled is 875 km. 4. If one travels 697 m by rail and 478 km by road, the total distance is 478 km. Q.23 A thin copper wire of length l metre increases in length by 2% when heated through 10°C. Which is not the percentage increase in area when a square copper sheet of length l metre is heated through 10°C (1) 12% (2) 8% (3) 16% (4) 4% Q.24 A body travels uniformly a distance of (13.8 ± 0.2) m in a time (4.0 ± 0.3) s. 1.

Its velocity with error limit is (3.5 ± 0.31) ms–1

2.

Its velocity with error limit is (3.5 ± 0.11) ms–1

3.

Percentage error in velocity is ± 4%

4.

Percentage error in velocity is ± 9%

DIRECTION (Q.25-Q.27) : Read the passage given below and answer the questions that follows : The internal radius of a 1m long resonance tube is measured as 3 cm. A tuning fork of frequency 2000 Hz is used. The first resonating length is measured as 4.6 cm and the second resonating length is measured as 14.0 cm. Q.25 Calculate the maximum percentage error in measurement of e. (a) 3.33% (b) 2.23% (c) 4.33% (d) 5.33% Q.26 Calculate the speed of sound at the room temperature. (a) 275 m/s (b) 376 m/s (c) 356 m/s (d) 330 m/s

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