Unit & Dimensions Questions and Answers

41 In Young s slits are illuminated wavelengths double slit experiment the 2 mm by a 8 mm c 4 mm and apart photons of 12000 2 10000 At what minimum common central distance from the bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other are two and b 6 mm d 3 mm

In one dimensional motion instantaneous speed v satisfies 0 v vo a The displacement in time T must always take non negative values b The displacement x in time T satisfies v T x v T c The acceleration is always a non negative number d The motion has no turning points 1

9 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 a 7 73 cm b 7 23 cm c 7 023 cm 2017 Gujarat d 7 073 cm

A vector of P lying on XY plane makes an angle of 60 with positive x axis Magnitude of its component along positive y axis is 12 unit Then magnitude of component of the vector Palong x axis is 1 2 unit 3 4 3 unit 2 8 unit 4 6 3 unit

Using dimensional analysis angular frequency o of surface waves on a lake as a function surface tension o water density Q and the wave number k 2 is the wavelength derived Assuming that the dimensionless coefficient is equal to two in SI units in this cas do find the value of group velocity v in m s where v g ok Use o 64mNm Q 320 kg m 1 cm

The period of oscillation of a simple pendulum is T 2 g Measured value of L is 20 0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90s using a wrist watch of 1s resolution The accuracy in the determination of g is a 1 b 5 c 2 d 3

Assignment 1 Dimensional analysis 1 If the units of energy force and velocity are 50 J 5 N and 2m s what will be unit of mass length a 2 The units of power force and time are 1 kW 1kN and 1 milli second Find th 3 What will be the value o

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well The error in his measurement of time is 8T 0 01 seconds and he measures the depth of the well to be L 20 meters Take the acceleration due to gravity g 10 ms and the velocity of sound is 300 ms Then the fractional error in the measurement 8L L is closest to 2 A 1 C 3 B 5 D 0 2

1 A potential difference is maintained across it Two cells are connected in series first to support one another and then in opposite direction The balance points are obtained at 50 cm and 10 cm from the positive end of the wire in the two cases The ratio of emfs is NEET 20167 a 5 4 c 3 2 d 5 1 through a resistance R varies b 3 4

v m s 10 10 20 10 20 30 t s The particle has a constant acceleration The particle has never turned around The particle has zero displacement in the interval 0 to 1 The average cheed in the interval 0 to 10 c is 5mk

57 For a normal eye the cornea of eye provides a converging power of 40D and the least converging power of the eye lens behind the cornea is 20D Using this information the distance between the retina and the eye lens of the eye can be estimated to be NEET 2013 a 2 5 cm b 1 67 cm 5 cm c 1 5 cm d

A calorie is a unit of heat energy in transit and it equals about 4 2 J where 1 J 1 kg m s 2 Suppose we employ a system of units in which the unit of mass equals a kg the unit of length equals 3 m the unit of time is y s Then the magnitude of calorie in terms of new units is 1 4 2a 28 22 2 4 2a 8 3 4 2a 18 22 1 20 12 2

The velocity time graph of an object is shown in the following figure 50 Velocity ms 5 8 8 8 8 40 30 20 10 B 0 5 10 15 20 25 30 35 40 45 50 Time s a State the kind of motion that object has from A to B and from B to C b Identify the part of graph where the object has zero acceleration Give reasons for your answer c Identify the part of graph where the object has negative acceleration Give reasons for your answer

36 The dimensions of the area A of a black hole can be written in terms of the universal gravitational constant G its mass M and the speed of light c as A GaM c Here a a 2 2 and y 4 b a 2 2 and y 4 c 3 3 and y 2 3 and and y 2 3 6 3 3

A neutral sphere of radius r and density p is placed in a uniform electric field E that exists on the earth s surface in the vertically upward direction If the atomic number and the mass number of the material of the sphere are Z and A respectively then the fraction of electrons t should be removed from the sphere for it to remain in equilibrium is Assume that the sphere is able to hold the necessary charge without an leakage Here NA Avogadro r pg A eEN Z matber 1 ma Total C Total gA eENA Z thongo B matr mathongo

The length of pendu 1 01m and time for 30 oscillations is mea sured as one minute 3 second Error in length is 0 01 m and error in time is 3 second The percentage error in the mea surement of acceleration due to gravity is 215 3 10 4 15

Which of the following is dimensionally correct 1 Pressure Energy per unit area 2 Pressure Energy per unit volume 3 Pressure Force per unit volume 4 Pressure Momentum per unit volume per unit time

A spherical body of mass m and radius ris 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 7 Dimensionally can be represented by 1 mr 6 n b V c 6 mrn g m 6 rv

35 If internal resistance of a cell is proportional to current drawn from the cell Then the best representation of terminal potential difference of a cell with current drawn from cell will be a V 1 B b d V V

6 up A thin wire of length when heated to a certain temperature increases its length by 1 A sheet of the same material of area 21 x l is heated to the same temperature percentage increase in area will be 1 4 2 2 5 32 4 1 5

Track OABCD as shown is figure is smooth and fixed in vertical plane What minimum speed has to be given to a particle lying at point A so that it can reach point C 1 2 Question Type Single Correct Type 60 m s A 100 m s B 320m 14 C

In the context of the accuracy of measurement and significant figures in expressing the results of the experiment which of the following is are correct 1 Out of the two measurements 50 14 cm and 0 00025 Amperes the first one has greater accuracy 2 If one travels 478 km by rail and 397 m by road the total distance traveled is 478 km 1 Only 1 is correct 2 Only 2 is correct 3 Both are correct 4 None of them is correct

A train is moving towards north At one place it turns towards north east her we observe that A The radius of curvature of outer rail will be greater than that of the inner rail B The radius of the inner rail will be greater than that of the outer rail C The radius of curvature of one of the rails will be greater D The radius of curvature of the outer and inner rails will be the same

The period of oscillation of a simple pendulum is given by T 27 where I is about 100 cm and is known to have 1 mm accuracy The period is about 2s The time of 100 oscillations is measured by a stopwatch of least count 0 1 s The percentage error in g is 1 0 1 2 1 3 0 2

The velocity of water waves v may depend upon their wavelength X the density of water p and the acceleration due to gravity g The method of dimensions gives the relation between these quantities as 1 v x g p 1 2 v x gp 3 v x gl 4 v x g 1 3

3 The actual mass of an object is 12345 grams A student measures the mass of the same object on an electronic balance and records the following measurements 1 24 g 1 23 g 1 28 g and 1 19 g Calculate the average measured mass as well as the percent error for this measured mass Are these measurements precise Are they accurato

QTwo tuning forks having frequency 256 Hz A and 262 Hz B Tuning fork A produces some beats per second with unknown tuning fork same unknown fork produced double beats per second from B tuning fork then the frequency of unknown tuning is A 262 B 260 C 250

25 A gas bubble from an explosion under water oscillates with 25 a period T proportional to PadE where P is the static pressure d is the density and E is the total energy of the explosion The values of a b and care 1 a 0 b 1 c 2 2 a 1 b 2 c 3 3 a 5 6 b 1 2 c 1 3 a 5 6 b 1 2 c 1 3 80 9 a 1 41 20 2 8 5 terayer forude gr ver the energe foren Stedene TPE P 3f1a bac M 12 1 METT 1 a 0 b 1 c 28 2 2 a 1 b 2 c 3 3 a 5 6 b 1 2 c 1 3 D MA 4 a 5 6 b 1 2 c 1 3 mc 3 E ML 1

In a new system of units the net force applied on a block of mass 10 kg moving with acceleration 10 m s is given as 100 unit of force When the same block is moving at a speed of 20 m s its kinetic energy become 20 unit of energy A liquid has a surface tension of 10 SI units What is the magnitude of its surface tension in new system 10 20 AM Y

15 The electric potential varies in space according to the faga fara fr 2x2 relation V 3x 4y A particle of mass 0 1 kg starts from rest from point 2 3 2 under the influence of this field The charge on the particle is 1 C Assume V and x y are in S I units The time taken to cross the x axis is 1 20 s 2 40 s dv 3 200 s 4 400 s 16 Electric Potential is zero at point 3d 43 V 3x 4y 0 1 kg finns ins farger fa 2 3 2 1 20 s 2 40 s 3 200 s 4 400 s 16 a V x y a grofera na wa 21 3 21 for a faga fava t F 95 d 10 x5

One second is equal to 1 1650763 73 time periods of Kr cloc 2 652189 63 time periods of Kr clock

When the resistance of the left gap and the right gap of a meter bridge are 111 56 Q and 1 Q and the null point is found at 99 8 cm When the resistances are interchanged in the gaps the null point is at 0 3 cm The end corrections of the bridge wire are A 0 2 cm 0 3 cm B 0 27 cm 0 42 cm C 0 60 cm 0 70 cm D 1 52 cm 0 87 cm

so that the angular speed about the axis of the rod is oo The angular momentum of the entire assembly about the point O is I see the figure Which of the following statement s is are true 4m 6 20 00 IIT JEE 2016 Advanced Question Paper Solution Paper II 7 A The magnitude of angular momentum of the assembly about its centre of mass is 17 ma 0 2 B The centre of mass of the assembly rotates about the z axis with an angular speed of 0 5 C The magnitude of the z component of L is 55 ma o

mitsa peed esa and y th kg is placed on a rough wedge which is fixed on an elevator moving upward with constant velocity 2 m s The block m is at rest w r t wedge Net reaction force on the block is 1 5 N 3 75 N 3 2 m 30 Insig en dojot viarono 2 10 N A 12 N 2 m s dot to

137 The tall cylinder is filled with viscous oil A round pebble is dropped from the top with zero initial velocity From the plot shown in fig indicate the one that represents the velocity v of the pebble as function of time t KUKE t a b c t d

The fossil bone has a 14C 12C ratio which is of that in a living animal bone If the half life of 14C is 5730 years then the age of the fossil bone is Question Type Single Correct Type 1 2 11460 years 156 117190 years

12 Which of the following relations can be derived by the dimensional analysis 1 Q Qoe t Rc 3 Y Asin a 1 and 2 c 3 and 4 2 2 t x 2 K 4 v 1 mv 2 Pr 8 n I b 2 and 3 d None of these Iw 2

The gravitational masses m and m seprated by a Gm1 m distance r is give by F force F between two where G is the universal gravitational constant What are the dimensions of G O M L T 2 O ML T 2 C O ML T 3 M L T 3 I p

For an endothermic reaction where AH represents the enthalpy of reaction in kJ mol the minimum value fo the energy of activation will be 1 less than AH 3 equal to AH 2 more than AH d gro

A number of capacitors each of capacitance 1 F and each one of which gets punctured if a potential difference just exceeding 500 volt is applied are provided Then an arrangement suitable for giving a capacitor of capacitance 3 uF across which 2000 volt may be applied requires at least 1 4 component capacitors 2 12 component capacitors 3 48 component capacitors

20 A new system of units is proposed in which unit of mass is a kg unit of length is m and unit of time is y s What will be value of 5 J in this new system a 5 2 c 5 8 b d 5 B 2 5 8

When a small sphere moves at low speed through a fluid the viscous force F opposing the motion experimentally is found to depend upon the radius r the velocity v of the sphere and the viscosity n of the fluid Expression of force is proportional to Hint n ML T

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 P S c 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 H W

3 If force F velocity V and acceleration A are taken as the fundamental units instead of mass length and time then which of the following gives the dimensions of the Gravitational constant in terms of F V and A

When a particle of mass m moves on the x axis in a potential of the form V z kz It performs simple harmonic motion The corresponding time period is proportional to as can be seen easily using dimensional analysis However the motion of a particle can be periodic even when its potential energy increases on both sides of x 0 in a way different from k2 and its total energy is such that the particle does not escape to infinitely Consider a particle of mass m moving on the x axis Its potential energy is V x ax a 0 for a near the origin and becomes a constant equal to Vo for lz X see figure If the total energy of the particle is E it will perform periodic motion only if m V x A M

A correct thermometer in Fahrenheit is introduced in a water bath along with a Celsius thermometer There readings observed are 86 F and 32 C The correction to be made to the Celsius reading will be Question Type Single Correct Type 1 2 5 C 22 C 3 1 5 C

A physical quantity is given as the function of x where x has the dimension of length If the dimension of i given by 0 which of the following equations are dimen sionally correct A do dx d o dx d o dx B do dx do dx 2 X 10 d o dx

18 Two tiny spheres carrying charges 1 8 C and 2 8 C are located at 40 cm apart The potential at the mid point of the line joining the two charges is a 3 8 x 10 V b 2 1 x 10 V c 4 3 x 10 V d 3 6 x 10 V 19 In the question numbe

For a hypothetical model total energy of an electron is given as Bv2 Total energy Ar BFte where r distance of electron F force on electron v speed of electron A Choose CORRECT dimensional formulae of C A MLT B ML T31 C MLT1 D ML T

A current carrying wire carries a current of 2A along the z axis which is out of the page while another wire carrying current of 4A in the same direction lies parallel to the first as shown in the figure Then around which loop linking both wires B d7 will be zero 2 1 3 4A clavit 010 en 8 bleit oben sm br bsens instanco 2A 4A0 2 P205 2A monye Bolesn 4A O 4 None of these