Unit & Dimensions Questions and Answers

4 In the determination of Young s modulus by using Searle s method a wire of length L 2 m and diameter d 0 5 mm is used For a load M 2 5 kg an extension 0 25 mm in the length of the wire is observed Quantities d and I are measured using a screw gauge and a micrometer respectively They have the same pitch of 0 5 mm The number of divisions on their circular scale is 100 The contributions to the maximum probable error of the Y measurement Y 4MLg Ald A due to the errors in the measurements of d and I are the same B due to the error in the measurement of d is twice that due to the error in the measurement of 1 C due to the error in the measurement of I is twice that due to the error in the measurement of d D due to the error in the measurement of d is four times that due to the error in the f 1

36 resistance A ring is made R 12 2 Find the points A and B as shown in should be connected so that the resistance R of the the figure at which a current carrying conductor sub circuit between these points is equal to S 1 11 38 A 1 4 B AIPMT Prelims 20 2 1 2

A quantity P is given as P A B C4D which brings maximum error in Pis 1 A 2 B 3 C 4 D The quantity

3 0 01 mm 4 0 02 mm If force F velocity v and kinetic energy E an taken as fundamental units then dimensional formu for time in them is 1 EFV 3 FvE in a new system of unit the unit of mass is 10 k 2 EF 4 EF 2

11 In the relation y ma m al ma of y is Given m mass a acceleration and Lis length 1 MLT 2 2 MT 43 the dimensions T

F a e 2 akt k t temperature A X distance The dimensions of Bis B D Boltzmann constant MLT 4 M L 2T MLT 2 M LT 1

A man moves in an open field such that after moving 10 m on a straight line he makes a sharp turn of 60 to his left The total displacement just at the start of 8th turn is equal to 1 12 m 2 15 m 3 17 32 m 4 14 11 m

61 15 The surface tension of a liquid is given as T a02 be where a and b are constants and 9 is absolut temperature Dimensions of a and b are 1 M LT K M L T K 3 M T K2 M T K TRUE 2 MIT K2 MITK 4 MILZTK MILT K2

In the circuit shown here the point C is kept connected to point A till the current flowing through the circuit becomes constant Afterward suddenly point C is disconnected from point A and connected to point B at time t 0 Ratio of the voltage across resistance and the inductor at t L R will be equal to 2 1 c 4 1 1 1 3 c A B R www

A coil of inductance 50 H and resistance 0 5 2 is connected to a battery of emf 5 V A resistance of 10 2 is connected parallel to the coil Now at some instant the connection of the battery is switched off Then the amount of heat generated in the coil after switching off the battery is 1 1 25 mJ 2 2 5 mJ 3 0 65 mJ

26 In a uniform electric field if a charge is fired in a direction different from the line of electric field then the trajectory of the charge will be a 1 Straight line 2 Circle 3 Parabola 4 Ellipse

es en 20 Three charges 4q Q and q are placed in a straight 2 line of length at points 0 and distance away from one end respectively What should be Q in order to make the net force on q to be zero 1 q 2 4q 3 q 4 2q LIE J 1M mr d 2312

But I have a doubt why can t it be option b If it isn t correct then please give an exampl e of a scalar which can take ve values 4 h e lowong rements is true la scala quantity s that is conserved in process e scara partir is het entire tea that can never t 1 Ascala quantity het e to another does not very from one point

If the speed v of a particle of mass m as function of time t is given by v A sin where A has dimension of 5 m length A the argument of trigonometric function must be a dimensionless quantity B Dimensional formula of oo is LT C Dimensional formula of k is MLT 2 D Dimensional formula of k m is T

English 36 37 38 Question No 41 39 40 In a problem an equation is given by A A O Velocity 2 VMV represent the physical quantity Kinetic energy Momentum Time Left 177 32 Force 41 42 cose In this problem Y Marks 4 1

The least count of a stop watch is s Two persons A and B use this watch to measure the time peri 5 of an oscillating pendulum Person A takes the time period of 30 oscillations and person B takes the ti period of 50 oscillations Neglecting all other sources of error we can say that Absolute error in measurement of one time period by A is greater than the of B B Absolute error in measurement of one time period by A is equal to that of B Accuracy in measurement of one time period by B is greater than that of A D Accuracy in measurement of one time period by A is equal to that of B

4 both 2 and 3 11 If velocity p acceleration q and density are taken as fundamental quantit Then the dimensional formula for kinetic energy k is 1 p82q3 2 p28a3 4 n 3 mage

Three concurrent forces of the same magnitude are in equilibrium What is the angle between the force Also name the triangle formed by the force as sides A 60 equilateral triangle B 120 equilateral triangle C 120 30 30 an isosceles triangle D 120 an obtuse angled triangle

5 Find the resultant of the following two vectors A and B A 40 units due east and B 25 units 37 north of west A 25 units 37 north of west C 40 units 53 north of west passo T B 25 units 37 north of east D 40 units 53 north of east

24 0 3 A vector B which has a magnitude 8 0 is added to a vector A which lie along the x axis The sum of these two vectors is a third vector which lie along the y axis and has a magnitude that is twice the magnitude of A The magnitude of A is 8 A 5 B 4 5 C 2 5 Infusib D 6 5

The sum of the magnitudes of two forces acting at a point is 16N The resultant of these force is perpendicular to the smaller force and has a magnitude of 8 N If the smaller force is of magnitude x then the value of x is A 2 N B 4 N C 6 N D 7 N

13 If energy E velocity V and time T are choser as the fundamental quantities the dimensiona formula of surface tension will be AIPMT 2015 1 E V 1 T 2 E V T 1 3 E V 1 T 4 E V T

2 8 marks Prof Saha gave the following problem to four students In this problem work done by a system on its surroundings is taken as positive A non ideal gas follows the Van der Waals equation of state P V nb nRT where P V and T denote the pressure volume and temperature respectively n is the number of moles R is the universal gas constant and a bare dimensional positive constants This gas expands adiabatically from an initial temperature T and volume V to a final temperature Ty and volume V The adiabatic process is described by an equation of the form f P V n a b a constant where a is a dimensionless number which is greater than 1 It is given that a in the ideal gas limit where is the adiabatic exponent What is the work W done by the gas in the process The four students solved the problem independently and gave for different answers Their answers were a W b W nR nR a 1 T T n a V V T T n a V V n R a 1 nR c W d W R T T w T T n a V V 1 Vj nb T 1 1 Vi nb Now Prof Saha had actually provided the exact expression of f P V n a b a to the students but could not remember it during evaluation Still he could determine that some or all of the four answers above must be incorrect based on general physical arguments alone Consider each of the four answers and give at least one reason for each of them showing why it is wrong or possibly correct Note that you are not required to give a correct expression for W or a detailed derivation for it in this question

move in a sion The 30 of bob is moved ngular ension point A block Ving Vo with velocity vo and collides elastically with block A of mass m and connected to another block B of mass 2m through a spring of spring constant K Find the value of K if Xo is the compression of the spring when velocities of A and B are same C Vo 1 mv Xo 2 2 3 2 3 mv 2 x 2 A 131 2 A 2 B smooth 4 mv 2 2x 2 2 2mvo WIN 2 Xo E 3 e6 60 35 In tw the 1 2

A quantity X is given by EL where At is the permittivity of free space L is a length AV is a potential difference and At is a time interval The dimensional formula for X is the same as that of A resistance B charge C voltage D current

The least count of a stop watch is 0 2 second It record 25 sec as the time of 20 oscillations of a pendulum Th minimum percentage error in the measurement of tim will be 1 0 8 3 0 2 2 0 4 4 0 1

11 If the sum of two unit vectors is also a unit vector then magnitude of their difference and angle between the two given unit vectors is 1 3 60 2 3 120 3 2 60 4 2 120

Q 43 A person walks 10m due East and then walks 5m at an angle 37 West of North How far is the person from the starting point AO 15m BO 3 5m 2 CO 67m

Q 3 In the circuit shown here the point C is kept connected to point A till the current flowing through the circuit becomes constant Afterward suddenly point C is disconnected from point A and connected to point B at time t 0 Ratio of the voltage across resistance and the inductor at t L R will be equal to Your Answer e 1 e Option 1 1 e C B R

1 Energy An object is moving through a liquid The viscous damping force acting on it is proportional to its velocity The dimensions of constant of proportionality are L F KX 1 MLT 2 MLT 3 M LT 1 4 MLT 1 the dimensional formula for

Reflection of Lights from Spherical Plane Mirrors 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 radian is 1 2 0 2 4 0 3 3 0 4 5 0 A short linear object of length lies along the axis of 2 Refr 3 Dis 4 Tot When it is fou beam 1 C 2 D 3 F

13 Speed of light in S I system is 3 x 108 m s In a new system unit of length is a km and unit of time is b second Then speed of light in new system of unit is 1 105 3 3a 105 2 4 b 105 3a 3b 105

In electromagnetic theory the electric and magnetic phenomena are related to each other Therefore the dimensions of electric and magnetic quantities must also be related to each other In the questions below E and B stand for dimensions of electric and magnetic fields respectively while eo and uo stand for dimensions of the permittivity and permeability of free space respectively L and T are dimensions of length and time respectively All the quantities are given in SI units 1 The relation between E and B is a E B L T b E B L T c E B L T d E B L T 2 The relation between eo and uo is a Ho eo L T c g LT Choose the correct answers from the below options a b c d 1 a 1 b 1 c A b g eo L T d ET LIIT 2 b 2 c 2 d

Consider that a particle is projected with velocity u 10 m s at an angle 0 60 with the horizontal and take value of g 10 m s Now answer the following questions 34 35 The radius of curvature of path of particle at the instant when the velocity vector of the particle becomes perpendicular to initial velocity vector is A C 20 3 3 40 3 3 m m B D The magnitude of acceleration of particle at that instant is A 10 m s C 5 m s 10 3 3 80 3 3 m m B 5 3 m s D 10 3 m s

The velocity v of water waves depends on the wavelength density of water p and the acceleration due to gravity g Deduce by the method of dimensions the relationship between these quantities 3

10N u measure two quantities as A 10 0 0 25 nd B 20 0 0 2 m We should report correct alue for AB as 14 1 0 3 m 11 1 0 4 m 2 14 1 0 15 m 4 14 1 0 2 m divisions of a vern in wh

Any vector in an arbitrary direction can always be replaced by two or three a Parallel vectors which have the original vector as their resultant b Mutually perpendicular vectors which have the original vector as their resultant c Arbitrary vectors which have the original vector as their resultant d It is not possible to resolve a vector

ML T A col 4 co M L T A 1 ML T A L T M L 7 3 ML T L T2 ML TA The dimensions of angular momentum latent heat and capacitance are respectively 2 MLT2 L T2 M L2T4A 4 ML T L T M L T A mass L The respective number of significant figures for the number 1 5 1 2

A square brass plate of side 1 0 m and thickness 0 005 m is subjected to a force F on its smaller opposite edges causing a displacement of 0 02 cm If the shear modulus of brass is 0 4 x 10 N m the value of the force F is 1 4 10 N 2 400 N 3 4 104 N 4 1000 N

8 Two blocks of masses 6 kg and 4 kg are connected by a rope of mass 2 kg are resting on a frictionless floor as shown in the following figure 4kg CBA 6kg 2kg F 60N If a constant force of 60 N is applied to 6 kg block then the tension in the rope at points A B and C are respectively given by 1 60 N 60 N 60 N 3 20 N 25 N 30 N 2 30 N 25 N 20 N 4 20 N 20 N 20 N

1 In the formula X 3YZ X and Z have dimensions of capacitance and magnetic induction respectively What are the dimensions of Y in MKSQ system 1995 2 marks a M L T Q c M LTQ b M L T Q d M L T Q

A current carrying coil is placed in a constant uniform magnetic field B Torque is maximum on this coil when plane of coil is A Perpendicular to B B Paralle to B C At 450 to B

The vector product of two vectors a and b is a vector c such that the magnitude of c is given by Olal lbl cose Olal lbl tane lal b cote Olal lbl sine 1 point

A block of wood of mass 2 6 kg is moved up along 8 9 m incline from rest by applying a horizontal force of 25 N If the incline makes an angle of 23 with the horizontal and the total work done on block to move it up the is 78 9 J calculate the magnitude of frictional force between wood and the incline Answer a 4 19 N b 15 5 N c 12 6 N d 6 79 N A B

A body is started from rest with acceleration 2 m s till it attains the maximum velocity then retards to rest with 3 m s2 If total time taken is 10 second then maximum speed attained is 1 12 m s 3 6 m s 2 8 m s 4 4 m s

his section contains 35 SINGLE CORRECT TYPE questions Each question has 4 choices 1 2 3 and 4 out of which only one is correct Read More he resistance of a wire is measured as 6 0 5 ohm The absoluto orror

A particle moves in space such that its velocity and acceleration at certain point is given by v 41 m s and a 61 2 6k m s The magnitude of component of acceleration in m s in the direction of velocity known as tangential acceleration is

4 Amount of substances The velocity of a particle is given by v Acos wt kx where x is position and t is time The dimensions of 1 LT 1 3 L T 2 k 30 is NCERT Pg 32 2 L T 4 L T Which of the following quantities have same dimensions as that of energy NCERT Pg 31

The position x of a body moving with uniform acceleration depends on time t as x 2t 6t The numbers 2 and 6 in the equations are 1 Dimensionless variable 2 Dimensional constant 3 Dimensionless constant 4 Dimensional variable 201 numbers toh dimensionless constant hote hai toh fir 2 and 6 dimesional constant kaise hue please solve and explain i am

Join the relation of physical quantities in Column I to the details given in Column appropriately Column I a Stress Strain b Dimensional formula for compressibility Column II i M L 1 T 2 ii M L T 2 iii Poisson s ratio iv Hooke s law