Unit & Dimensions Questions and Answers

Time has a direction it can never be negative still then it is a scalar and vector quantity Which not a statement is the correct explanation for the time not being to be vector a It is not obeying law of parallelogram addition b It has unique direction c Both a and b d None of the above

Q 2 A particle of mass m is attached to a rod of length e and it rotates in a circle with angular velocity o An observer P is rigidly fixed on the rod at a distance L 2 from the centre The acceleration of m and the pseudo force on m from the reference frame of P must be respectively A zero zero B zero mo L 2 P O L m C w L mo L 2 D zero mo L

1 6 The acceleration of a particle is given by the relation as a kv 2 where k is a constant The particle starts at x 0 with a velocity of 16 m s and when x 6 the velocity is observed to be 4 m s Find the velocity of particle when x 5 m and the time at which the velocity of the particle is 9 m s 0173 1

Volume flow per unit time Q in a tube depends on velocity of flow v cross section area of tube A and density of liquid p as vX AY p where x y z are real numbers Select correct alternative s Q X X 1 y 1 z 1 Z 0

1 ERCISE III Analytical Questions In a particular system the units of length mass and time are chosen to be 10 cm 10 g and 0 1 s respectively The unit of force in this system will be equal to 1 0 1 N 2 1 N 3 10 N 4 100

Planck s constant h speed oflight 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 hG 3 2 a c hc G b d hG 5 2 Gc h 2

The equation of the stationary wave is Arms 2 ct 2xC cos 2xx COS y 2A sin Which of the following statements is wrong A the unit of ct is same as that of B the unit of x is same as that of C the unit of 2 c is same as that of 2 x t D the unit of c is same as that of x Asked by 2286885 aesl id Standard XII Stream NEET Jul 14 2021 at 5 29 PM Add your responses Type Text Type your answer here OR you can upload an attachment from the option below Attachment size should be 5MB or less Keep the format in jpg or png or pdf or doc or docx only Add Attachment

A force acts on a body of mass 15 kg initially at rest If the instantaneous power due to the force at the end of the third second is 5 W then the instantaneous power in W at the end of the fourth second will be Options 1 2 3 6 33 6 67 6 29

The zero of main scale matches with zero of Vernier scale 9th division of main scale matches with 10th division of Vernier No other match is present After sliding zero of Vernier is found to be in between 3th 4th divisions of main scale 5th division of Vernier matches with xth division of main scale The value of x is Given 10VSD 9MSD A 8 B 7 C 6 D 5

5 Amachine in an amusement park consists of a cage of the end of Arm hinged at O The cage revolves along a vertical circle of radius r ABCDEFGH about its hinge O at constant linear speed v gr The cage is so attached that the man of weight W standing on a weighing machine inside the cage is always vertical Then which of the following is correct A The weight reading at A is greater than the weight reading at E by 2W B The weight reading at G W C The ratio of the weight reading at E to that at A 0 D The ratio of the weight reading at A to that at C 2

resonates in 1st resonance with a tuning fork When it is filled with nitrogen gas N it resonates with the same tuning fork in 1st resonance when water column is shifted down by 10 cm Take 5 2 25 CHOOSE INCORRECT STATEMENT A Wavelength of sound in Ozone is approximately Im B Wavelength of sound in Nitrogen is approximately 16m yana IIT Academy 13 07 21 OSR IIT CO SC ExPT 1 Q P C For second resonance in Ozone gas the water column should be shifted down by 60cm

Which of the following equation is dimensionally inconsistent Here 1 lo L m mo M 1 10 sin m sin mo X2 1 lo sin m mo cos m mo X3 1 lo log m m mo log m m 1 1 log m m sin m m

Q 21 The lengths of sides of cuboid are a 2a and 3a If the relative percentage error in the measurement of a is 1 then the relative percentage error in the measurement of volume of cube is

Which of the following functions of time represent a SHM and b Periodic but not SHM c Nor motion i sin cot cos cot iv log ot ii sin cot cos 2 wt sin 4 cot v sin ot cos ot iii e ot vi sin cot

Which of the following relations cannot be obtained by using dimensional analysis where F represents force u represents mass per unit length T represents surface tension P represents momentum L represents loudness I represents intensity I represents reference intensity d represents density represents length r represents radius h represents height and g represents acceleration due to gravity v represent frequency Dimension involves M L T only A V x C hx EVE T rdg B L x 10 log p2 M D K E x

16 A screw gauge gives the following reading when used to measure the diameter of a wire Main scale reading 0mm circu lar scale reading 52 divisions Given that 1mm on main scale corresponds to 100 di visions of the circular scale The diameter of the wire from the above data is 1 0 052cm 3 0 005cm 2 0 026cm 4 0 52cm

In a new system of units unit of mass is taken as 50 kg unit of length is taken as 100 m and unit of time is 1 minute What will be weight of a body in this system if in S I system its weight is 10N A 7 2 C 840 B 72 D 7200 2

Force on a particle is given by F a log xt where t is time and x is distance then a and B are respectively A LT LT B MLT LT C ML T dimensionless D MLT2 dimensionless 1 X F a log xt RT a B 3 A LT LT B MLT2 LT1 C MLT faiata D MLT2 fa I

Power delivered by a force is given by relation B t where t is time The P 5 e B dimensional formula of a and B will be A MLT 2 LT B MLT T C ML T T D LT T

iv A flat circular coil of 200 turns of diameter 25cm is laid on a horizontal table and connected to a ballistic galvanometer The complete circuit is having resistance of 80022 When the coil is quickly turned over the spot of light swings to a maximum reading of 30 divisions When a 0 1 F capacitor charged to 6 V is discharged through the same ballistic galvanometer a maximum reading of 20 divisions is obtained Calculate the vertical component of the earth s magnetic induction 0 37 10 T

A particle of mass 3 kg is moving along x axis and its position at time t is given by equation x Work done by all the forces acting on it in time interval f 0 tot 3 sis 1 144 J 2 72 J 3 4 108 J 216 J 2 5 m

16 Correct dimensional formula for the permeability of free space is 1 MLT A 2 3 M L T 2A NCERT Pg 198 2 ML T 2A 4 ML T 3A2 19

12 The maximum value of the magnitude of the resultant of two vectors Panda is 24 units and the minimum value of the magnitude of their resultant is 4 units What is the ratio of the magnitudes of the two vectors Pand Q 8 mor 4 200 b te d 7

a b c d Q 21 For Question 21 25 two statements are given one labelled Assertion A and other Reason R Select the correct answer to these Question from the codes a b c and d as given below Both A R are true R is correct explanation of A Both A R are true but R is NOT the correct explanation of A A is true but R is false A is false R is true Assertion Beacon Classical Physics deals mainly with macroscopic phenomena conic ular and much

4 1 The dimensional formula of angular acceleration Question Type Single Correct Type 1 MOLOT 1 2 MOLOT 2 English Review Q 3 MOL T 2 4 MOLIT 1 O

plavi A particle of mass m is projected with a velocity V making an angle of 45 with the horizontal The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height h is A zero B m V 4 2 g C mV 2gmon D m 2gh 13

4 27 A narrow beam of identical ions with specific charge q m possessing different velocities enters the region of space where there are uniform parallel electric and magnetic fields with strengths E and B at the point O The beam direction coincides with the x axis at the point O A plane screen oriented at right angles to the x axis is located at a distance from O Find the equation of trace that the ion leaves on the screen Demonostrate that at z 1 it is the equation of a parabola Ans 2 B 1 q y 2mF

n a new system of units mass acceleration and frequency are taken as fundamental units If unit of mass is 10g unit of acceleration is 5 m s and unit of frequency is 2 sec in a new system units find the value of 1 J in this system

In a new system of units mass acceleration and frequency are taken as fundamental units If unit of mass is 10g unit of acceleration is 5 m s and unit of frequency is 2 sec in a new system of units find the value of 1 J in this system

Three vectors A B and C are of magnitudes 10 units 5 unit and 10 unit respectively If they make angles 30 120 and 300 with X axis and all lie along the X Y plane then determine the magnitude of the resultant A 5 3 LC B 5 5 R 10 5

A wheel rolls without sliding along a horizontal road The velocity of the centre of wheel is v then the magnitude velocity of centre of wheel with respect to instantaneous axis of rotation will be A Zero B v Dai P R C 2v D

Which of the following is correct order 1 1 AU 1 ly 1 parsec 1 fermi 2 1 ly 1 AU 1 parsec 1 fermi 3 1 parsec 1 ly 1 AU 1 fermi 4 1 parsec 1 AU 1 ly 1 fermi 42 1 1 AU 1 ly 1 parsec 1 fermi 2 1 ly 1 AU 1 parsec 1 fermi 3 1 parsec 1 ly 1 AU 1 fermi 4 1 parsec 1 AU 1 ly 1 fermi

6 A weighing machine provides measurement of mass in kg in four trials as 50 00 50 20 50 12 and 50 08 respectively then 1 Mean absolute error is 0 06 2 Fractional error is 0 002 3 Percentage error is 0 2 4 Fractional error is 0 01 The phenomenon of scattering of light by change in wavelength is called 1 Chadwick scattering 2 Ramanujan scattering uton s scattering

7 Two rods A and B of radii in ratio 1 2 and length ratio 2 5 are placed between rigid supports with no scope for expansion The material of both rods is same Now if both the rods are heated to produce the same temperature rise then the ratio of thermal stress developed in A and B is 4 1 1 3 1 4 2 1 2 4 1 8 maximum length of a uniform wire

According to Maxwell distribution law the probability function representing the ratio of molecules at a particular velocity to the total number of molecules is given by 3 m 2 k 2 my 4 v 2KT f v k Where m is the mass of the molecule v is the velocity of the molecule T is the temperature k and k are constants The dimensional formulae of k is A L T2 B L TK 3 2 C L TK 3 2 D L TK 3 2

Suppose we employ a system in which the unit of mass equals 100 kg the unit of length equals 1 km and the unit of time 100 sec and call the unit of energy as eluoj joule written in reverse order then what is the relation between eluoj and joule A 1 eluoj 10 joule B 1 joule 10 eluoj C 1 eluoj 10 joule 103 aluoi D 1 joule ion

ladder circuit between terminals A and B as shown in the figure is 20 Ao www Bo 402 1 2 2 2 2 2 2 92 3 3 3 2 402 www 82 www 80 160

Consider three physical quantities x y and z Operations x y and y z are valid with these physical quantities Which of the following conclusions can you make The operation x z is also valid O If dimension of any of the three is known dimension of other two can be predicted If dimension of product of any two of them is known dimension of all of them can be predicted If dimension of quotient of any two of them is known dimension of all of them can be predicted

A spherical body of mass m and radius r is 7 allowed to fall in a medium of viscosity n The time in which the velocity of the body increases from zero to 0 63 times the terminal velocity v is called time constant t Dimensionally t can be represented by mr 61 6 mm m 3 6nrv 4 None of the above Write down the number of significant figure in 8 guard 0 634 Fandis 1 far fin t mr 6am r ford f 6amm m 3 Gan 4 3 eff 0 04320 N m en ferfery Pidal 4 V cal

2 5 If speed V area A and force F are chosen as fundamental units then the dimension of Young s modulus will be 1 FA V 3 3 FA V 2 FA V 4 FA V

10 Physical World Units D In a given system of units 1 unit of mass 2 kg 1 unit of length 5 m and 1 unit of time 5 s this system 1 N represents 5 2 units of force e of force 2 units of force 5 4 NI 2 units of force

Reflection of Light by Spherical Mirrors Plane 1 A driving mirror consists of a cylindrical mirror of radius of curvature 10 cm and the length over the curved surface is 10 cm If the eye of the driver be assumed to be at a great distance from the mirror then field of view in radan is 1 20 2 4 0 3 3 0 4 50 Sol Answer 1

c 0 2 d 0 8 99 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 newtons and weight in water is 4 00 0 05 newtons Then the relative density along with the maximum permissible percentage error is a 5 0 11 b 5 0 1 d 1 25 5 c 5 0 6 00 The length of a cylinder is measured with 1

3 lo 8 3 A man is walking on a horizontal of 5 km h and the rain appears to be fallin vertically at 5 km h to him The magnitude velocity of rain with respect to the ground is NCERT pg 1 5 km h 3 10 km h 2 5 2 km h 4 4 km h

3 2Rsin 15 4 Rsin 15 27 Consider the following two statements a Virtual image cannot be photographed b Virtual image can be seen by an obse The incorrect statement s is are 28 1 Only a 3 Both a and b calorimeter ntains 2 Only b 4 Neither a ne 100 100 g of ia at

18 The electric current in a circuit as a function of time t is given by 1 e where Vis voltage The dimensional formula of A and B are respectively 1 ML T A T 3 ML TA1 IT 2 M L T A T 4 IM L T 2A LIT

In an experiment on Ohm s law voltage drop across a resistor has been measured as V 100 5 volt and current through the resistor has been measured as 10 0 0 2 ampere The permissible error in calculation of R is

1 In a new system of unit unit of time is 10 s unit of mass is 5 kg and unit of length is 20 m In this system unit of energy is equal to 1 20 J 2 1 20 A Medical

75 The smallest division on the main scale of a vernier callipers is 1 mm and 10 vernier divisions coincide with 9 main scale divisions While measuring the diameter of a sphere the zero mark of the vernier scale lies between 2 0 and 2 1 cm and the fifth division of the vernier scale coincide with a scale division Then diameter of the sphere is a 2 05 cm b 3 05 cm c 2 50 cm d None of these

65 A workman measures as accurately as possible the length and internal diameter of a straight copper pipe The length is approximately 600 cm and the internal diameter is approximately 2 cm What is the best combination of instruments for the work man to use A B C D a A Internal Diameter Ruler Ruler Vernier Calipers Vernier Calipers Length Ruler Tape Ruler Tape b D