Unit & Dimensions Questions and Answers

Knowledge Sections Q No 2 Which of the following errors are generally distributed in accordance with the Gaussian distribution A Controllable errors B Calibration errors C Avoidable errors D Random errors

24 The number of particles crossing per unit area perpendicular to Z axis per unit time is given by N N Z Z N D where N and N are the number of particles per unit volume at Z and Z respectively What is the dimensional formula for D 1 MOL T 2 MOL T 1 3 MOL T 1 4 IMO T 1

length time period of oscillation T 2 0 1 s Calculate the value of g within the error limits assuming that true value of g 9 8 m s2 1 Point Given that the formula for time period is T 2m 2 7 9 8 0 1 m 9 8 1 0 9 8 0 9 9 8 0 99

22 Test which of the following equation is dimensionally correct Given that V is volume P is pressure r is radius of the tube t is time n is coefficient of viscosity and I is the length of the tube 1 Point Pri 8ql OV Pr 1 OV 2P 1

Choose the incorrect statement out of the following 1 Every measurement by any measuring instrument has some error 2 Every calculated physical quantity that is based on measured values has some error 3 Ameasurement can have more accuracy but less precision and vice versa 4 The percentage error is different from relative error

The physical quantity Energy Density has same 1 dimensional formula as 1 Pressure 2 Stress 3 Young s modulus of elasticity 4 All of these 1 2 sfarger 3 4 a on facita ya fenu farita

9 When n small drops are made to combine to form a big drop then the big drop s 1 Potential increases to n 1 3 times original potential and the charge density decreases to n 3 times original charge 2 Potential increases to 2 3 times original n potential and charge density increases to 3 times original charge density 1 3 3 Potential and charge density decrease to n times original values 4 Potential and charge density increases to n times original values

figure shows a spherical hollow inside a solid sphere to radius R the surface of the hollow passes through the centre of the sphere and touches the right side of the sphere The mass of the sphere before hollowing was M With what gravitational force does the hollowed out lead sphere attract a small sphere of mass m that lies at a distance d from the centre of the lead sphere on the straight line connecting the centre of the spheres and the hollow AMU 2013 R d m

Two wires are bent shown as joint circle with radius r in xy plane The upper half has resistance of 2R 22 and the lower half of RQ A current I is passed into circle as shown The magnetic field at centre is 2RQ Hol 1 HOT K r 3 zero RQ y L 2 Ho k 2r HoI Or k X

This questio O only In a plane electromagnetic wave the directions of electric field and magnetic field are represented by and 2 2 respectively What is the unit vector along direction of propagation of the wave

efficients Example 14 2 Which of the following functions of time represent a periodic and heb non periodic motion Give the period for ht each case of periodic motion o is any t positive constant Imp The ime ent ons ce 1 sin ot cos ot J Sot cos 2 ot sin 4 tot ni iv loot Ancuer Ark A and A motion is A Fig 14 3 displace varies v where CV

19 A vernier calliper has 20 divisions on the vernier scale which coincide with 19 on the main scale The least count of the instrument is 0 1 mm The main scale divisions are of 1 0 5 mm 3 2 mm 2 1 mm 4 1 4 mm

A capacitor of capacitance 5 F is connected to a source of constant emf of 200V for a long time then the switch was shifted to contact 2 from contact 1 The total amount of heat generated in the 50002 resistance thereafter is 1 1 32 J S F HH 50002 www 200V 30002 2 3 32 J

Experiments reveal that the velocity v of water waves may depend on their wavelength wavelength has dimensions of length as X density of water p as ph and acceleration due to gravity g as g then value of a b c

In a new system of units mass acceleration frequency are taken as fundamental units If unit of mass is 100 g unit of acceleration is 2 m s and unit of frequency is 4 sec in this new system of units then the value of 10 J in this new system is Kx 100 Fill K in OMR Sheet Erno 1 00 a vale

The kinetic energy of a particle varies according to Av relation K Here x is the distance and v B x is the velocity The dimensional formula of AB is 1 ML TO 2 ML4T0 3 ML4T 4 M L T0

The maximum value of the magnitude of the resultant of two vectors P and 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 P and Q O O C 3 4 4 5 615

1 The resultant of M and N is perpendicular to The what is the angle between M and N M M N M 4 Sin M 1 cos 3 sin 2 cos N

Which of the following is incorrect statement Question Type Single Correct Type 1 2 3 A dimensionally correct equation may be correct A dimensionally correct equation may be incorrect A dimensionally incorrect equation may be correct A dimensionally incorrect equation is

P 1N unit of force Q 1 m s List NOI CO unit of speed OP 20 1 3 R 1 3 S 1 3 4 OP 20 134 R 1 3 S 1 3 P 30 1 3 R 1 3 S 1 3 1 3 2 R 1 kg m s unit of momentum 3 M 1kg L 2 S 1 J unit of energy P 4 0 2 3 R 23 S 2 3 4 List II M 1kg L 2m T 3s 3 2 M kg L 1m T 1s 8 m T 1s 4 M 2kg L 2 m T 3s 5 None of above

01 02 03 04 05 06 07 08 09 10 T Which of the following is incorrect statement Question Type Single Correct Type 1 2 3 4 A dimensionally correct equation may be correct A dimensionally correct equation may be incorrect A dimensionally incorrect equation may be correct A dimensionally incorrect equation ir in net

The electric field of an electromagnetic wave in free space is given by E 10cos 10 t kx Vim where t and x are in seconds and metres respectively It can be inferred that a The wavelength 2 is 1884 m b The wave number k is 0 33 rad m c The wave amplitude is 10 V m d The wave is propagating along x direction Which one of the following pairs of statements is correct AIPMT Mains 2010 1 c d 2 a b 3 b c

A wave is propagating along x axis in a medium so that displacement y of particle at any position x and at any time t is given by y A Dimension of b is T C Dimension of C is L ze b where a b and c are constants Choose the correct option s B Dimension of a is LT2 D b c is dimensionless

simultaneously on a body keep it in translational equilibrium determine numerical value of b a Given thatA B C If A 4 B 5 and C 61 The angle between A and B in degree is If in a new system unit of length is 2m unit of time is 3s then x is the numerical value by which gravitational acceleration g 10 m s is represented in new system of unit Fill the value of X

Which of the following is incorrect statement O A dimensionally correct equation may be correct O A dimensionally correct equation may be incorrect O A dimensionally incorrect equation may be correct A dimensionally incorrect equation is incorrect

5 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 3 10 N 2 IN 4 100 N

Equilibrium constant for the reaction N 02 2NO at 3500 K is 0 0841 How much part of equilibrium mixture of N and O has been converted into nitric oxide N2 and O2 initially taken in 1 1 mol Question Type Single Correct Type 1 0 20 2 0 28 3 0 127

A famous relation in physics with many printi errors relates the moving mass m with rest ma for an object moving with speed V is written as m 1 2 no b 1 2 Dimensional formula of no and b are respectively c is speed of light 1 M LT 1 3 M121 T 11 2 M L T 2 A M 21 12T 21

The alternating current in a circuit is described by the shown in Fig 7 4 Show rms current in this graph I A 32 T do toto 2 T Fig 7 4 2T t load wh type of th 25 Explain alternati 26 Explain increasi 7 27 An ele 223V How does the sign of the phase angle o by which the sup oltage leads the current in an LCR series circuit change as supply frequency is gradually inoro of te ta

5 The position of a particle at time t is given by the relation x t 1 e dd where vo is a constant and a 0 The dimensions of vo and a are respectively 1 MOL T 1and T1 2 M L T and T1 3 MOL T and LT 1 10 1T1 and T

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 1 2 1 2 a G h 2c 5 2 C 1 2 1 2 c G 2 2 3 2 2 1 2 b G 2 2 2 d G 2 21 21

If the dimension of time are expressed as Gachy then the values of a and y are G Universal Gravitational Constant c Speed of light h Planck s constant A B C 1 1 22 1 NI 2 1 9 52 5 1 2 2 1

A physical quantity of the dimensions of length that e can be formed out of c G and is c is velocity 4 0 of light G is the universal constant of gravitation and e is charge a c G e c G C 4 E0 e 4 EO 71 2 b d 1 e c G4 EO 12 10 G e 4 EO 71 2 71 2

In the given figure the capacitance of capacitor is C The left plate of the capacitor is given charge Q and right plate is uncharged Then choose the CORRECT statement s K A The amount of charge that will flow through the battery till the steady state is reached when the switch K is closed will be C 2 B The charge appearing on the inner face of the left plate at steady state is Ce C The charge appearing on the innerface of the right plate at steady state is C 2Q 30 D If then work done by cell after closing the switch is

46 A physical quantity f depends on the dimensionful quantities x and y as follows f Ax Bexp cy Which of the following do not have the same dimensions A f and B 1 B c and y l C x and B A D x and A

The speed v of transverse waves travelling on a string depends on tension T with which the string is stretched and mass per unit length m of the string Using dimensional considerations obtain the expression for v in terms of T and m A body starting from rest has an acceleration of 20 ms 2 Calculate i distance travelled by body in 8 sec ii its velocity after travelling of 10 m iii distance travelled by it in 10 s

When a charged capacitor is connected across an inductor the current in the circuit varies with time as Q Locos Ct JLC LC capacitor L inductance C capacitance Then COS t where Q is initial charge on Dimensions of LC is T Dimensions of Q is AT Dimensions of Dimensions of LC is A ixyLC is AT

Let o denote the dimensional formula of the permittivity of the vacuum and po that of the permeability of the vacuum If M mass L length T time and current then M MALBTCID then value of A B C D is Afa Ayarham famu Afa famu ya s uzkagu M T 34 1 MAL TCID fa a MALBTCIDA B C D ch ATA

4 The number of particles crossing per unit area perpendicular to Z axis per unit time is given by N D N N Z 2 where N and N are the number of particles per unit volume at Z and Z respectively What is the dimensional formula for D 1 M L 1T 2 MOL T 3 MOL T 1 4 M L T 3 A screw gauge there are 50 c ofos re 0 65 x 0 1 100 104 The pitch of t S 100 10 100x1 1 0 25 m 3 1 0 mm Time int following 1 25 s What

If area of each plate is A and separation between the in plates is d then the reciprocal of capacitance of the earrangement shown in figure will be erit li VS 2 A K K 1 d 2 K K d 2 K Kisa K 1 K 1 d 3 K K 2K K A ed lliw 4 n A K K 2 d 2 K K SA d d A A K K

A screw gauge gives the following readings when used to measure the diameter of a wire Main scale reading 0 mm Circular scale reading 52 divisions Given that 1 mm on main scale corresponds to 100 divisions on the circular scale The diameter of the wire from the above data is 1 0 26 cm 2 0 052 cm 3 0 52 cm 4 0 026 cm

If units of length mass and time are doubled 2 Unit of force 13 A remains same B will be doubled C will be halved D will be quadrupled G 6 67 1 0 1 N m kg 2 becomes A 6 67 10 new units B 13 34 10 1 new units C 6 67 10 22 new units

Q 1 The main scale of a spectrometer is divided into 720 division in all If circular vernier scale consists of 30 divisions the least count of the instrument is Given 30 vernier divisions coincide with 29 main scale divisions 1 0 1 3 1 2 1 4 01

A spaceship is moving away from speed 0 03c where c is speed of light in air The spaceship emits signal of frequency 6x107 Hz Frequency of signal observed by the observer on Earth will be 1 1 2 x 107 Hz X 3 4 8 x 107 Hz 2 1 8 107 Hz 4 5 82 x 107 Hz 11 130 T

16 Choose the correct statement NCERT Pg 33 1 A dimensionally correct equation need not be an actually correct equation 2 A dimensionally correct equation may be an actually correct equation 3 A dimensionally incorrect equation may be correct 4 Both 1 and 2 19 to 10 9 assum 10 6 to 1 0 1 2 0 0 3 0 00

15 Each side of a cube is measured to be 6 372 m The total surface area of cube with appropriate significant figures is NCERT Pg 32 1 2 5 10 m 3 243 6 m 2 2 10 m 4 251 3207 m 16 Choose the correct statement 10 19

Q 25 A physical quantity A is dependent on other four physical quantities p q r and s HOP 5 as given below A OH pq 02 V The percentage 2 3 rs error of measurement in p q r and s are 1 3 0 5 and 0 33 respectively then the maximum percentage error in A is

3 n al 40 11 The value of gravitational constant is G 6 67 x 10 11 Nxm kg Suppose we employ a new system of units in which unit of mass is a kg the unit of length m and the unit of time is y s The value of gravitational constant in terms of new units NCERT Pg 35 is 1 6 67 x 10 11 B y 2 6 67 x 10 11 a 1 B 3 6 67 x 10 11 a 4 6 67 x 10 11 a 1 B y 15 1 93 s 1 99 s 2 06 s 2 accurate way measurement with error more 1 2 00 0 05 s 3 2 0 0 06 s Each side of a cube 6 372 m The total surfa appropriate significant f 1 2 5 10 m 3 243 6 m 2 PAI DUAL CAMERA 16 Choose the correct si

Three physical quantities A B and C are related as A B C then Dimensions of A B and C are same Dimensions of A B and C are different Dimensions of A and B are same but dimensions of A and C are different Dimensions of B and C are same but dimensions of A and C are different

A student performs an experiment for determination of g la 1m and he commits an error of Al For T he takes the time of n oscillations with the stop watch of least count AT and he commits a human error of 0 1sec For which of the following data the measurement of g will be most accurate Al AT Amplitude of oscillation A 5 mm B 5 mm C 5 mm D 1 mm 0 2 sec 0 2 sec 0 1 sec 0 1 sec n 10 20 20 50 5 mm 5 mm 1 mm 1 mm 47 l T