Unit & Dimensions Questions and Answers

The SI unit of intensity of wave is 2 a W m W m b Jm s c 2 d Jm s U

second sphere due to the first Check that the ratio ke G mm is dimensionless Look u of Physical Constants and determine the value of this ra does the ratio signify

10 A 2 25 mm Dipole moment Electric flux The number of circular divisions on the shown screw gauge is 50 It moves 0 5 mm on main scale for one complete rotation and main scale has 1 2 mm marks The diameter of the ball is B 2 20 mm C 1 20 mm lectric field 25 D 1 25 mm

In an electrical circuit potential difference V 8 0 0 8 V and current 2 0 0 2 A The value of resistance R with error limits is 4 0 1 Q 4 0 0 8 0 4 0 0 2 Q Read More 40 06 0

The force of interaction between two atoms is given by XP 2 where x is the distance k is the F a exp 2 a M L T 2 c MOL T4 akt Boltzmann constant and T is temperature and a and are two constants The dimension of Bis JEE Main 2019 46 M LTA d MLT 2

Question 12 A Xt Yt 2 The radioactivity of a sample is X at a time t and Y at a time t If the mean life of the specimen is T number the of atoms that have disintegrated in the time interval t2 t is B X Y C M M 4 00 X Y T N M 1 00 9

At time t 0 a 2290 kg rocket in outer space fires an engine that exerts an increasing force on it in the x direction This force obeys the equation F At where t is time and has a magnitude of 781 25 N when t 1 37 s Choose the correct Sl units of constant A O s N ON s

5 With the usual notation the following equation 1 S u a 2t 1 is 1 Only numerically correct 2 Only dimensionally correct 3 Both numerically and dimensionally correct 4 Neither dimensionally nor numerically correct

In the cube of side a shown in the figure the vector from the central point of the face ABOD to the central point of the face BEFO will be Z JEE Main 2019 a a i k Jby a c a k 1 d a k A KD X B 4016 O a 0 E Ha a a 2 2 F Y

4 The resultant of two vectors P and Q is R If the magnitude of Q is doubled the new resultant becomes perpendicular to P Then the magnitude of R is Kerala PET 2009 a P Q c P e P Q Lib Q d P Q 2

Two vectors A and B have equal magnitudes The magnitude of A B is n times the magnitude of A B The angle between A and B is JEE Main 20191 a sin b cos Vc cos 2 1 1 d sin n n 1 n 1

10 An arbitrary vector can be expressed as a sum of three mutually perpendicular unit vectors each multiplied by scalar constant equal to 1 a same scalar constant b d some scalar constant scalar constant equal to 1

The dimensions of the quantities in one or more of the following pairs are the same Identify the pair s a Torque and work b Angular momentum and work c Energy and Young s modulus d Light year and wavelength

The physical quantity electric potential V has dimensions M LbTCA and capacitance C has dimensions MSLITSA Then a b c d ef g his Answer

The time period of a body undergoing simple harmonic motion is given by T p DSC where p is the pressure D is density and S is surface tension The values of a b and c respectively are A 1 2 3 2 B 3 2 1 2 1 C 1 1 2 3 2 D 3 2 2 1

If the dimensions of a physical quantity are given by M Lb Ts then the physical quantity will be a velocity if a 1 b 0 c 1 b acceleration if a 1 b 1 c 2 c force if a 0 b 1 c 2 d pressure if a 1 b 1 c 2 O A O B O O O C

The figure shows a Young s double slit experimental setup It is observed that when a thin transparent sheet of thickness t and refractive index u is put in front of one of the slits the central maximum gets shifted by a distance equal to n fringe widths If the wavelength of light used is 7 t will 2019 Main 9 April 1 be

Q 45 For a normal eye the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D using this information the distance between the retina NEET 2013 and the cornea eye lens can be estimated to be

The mass of a cylindrical body depend on density d of material its diameter D and length L as M d DY LZ If maximum percentage error in measurement of density diameter and length are m n and respectively then maximum percentage error in calculation of mass is O m 1 n O mx yn lz m X n 1 Y Z mx ly nz

errors percentage in the measurement of mass and speed are 2 and 3 respectively How much will be the maximum error in the estimation of kinetic energy obtained by measuring mass and speed 5 The a 11 c 5 b 8 d 1

A conducting loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides A magnetic induction R constant in time and space pointing perpendicular and into the plane of the loop exists everywhere The current induced in the loop is

17 A particle moves on a given straight line with a constant speed v At a certain time it is at a point P on its straight line path O is a fixed point Show that OP xu is independent of the position P

X The position of a particle varies with time as x t 1 e t where Vo Vo B is a positive constant and 0 Dimensions of Vo and 3 are respectively O MOLT and T MOLT and T MOLTO and T 2 M L T and T

From the equation tan 0 rg one can obtain the angle of banking 0 from vertical for cyclist taking a curve the symbols have the usual meanings The equation is 1 both dimensionally and numerically corre 2 neither numerically nor dimensional correct 3 dimensionally correct only 4 numerically correct only

5 Check the correctness of the relation S ut at where u is initial veloci acceleration t the time and S the displ 1 Dimensionally correct 2 Dimensionally incorrect 3 Can t explain 4 Data insufficient

Select the incorrect are 1 0 06900 has 4 number of significant figur 2 0 6900 has 4 number of significant figur 3 6 900 has 2 number of significant figu 4 6 900 kg has 4 number of significant figu

om In the figure given below the acceleration of block P is ap 15i 15 under the action of external force Then acceleration of wedge Q is P always remain in contact with Q AY 1 6i 3 10 37 Q 2 15 4 5i X ET

Refer to figure 2 E1 Find a the magnitude b x an y components and c the angle with the X axis of th resultant of OA BC and DE Y 1 O 2 0 m 30 A 90 1 0 m 60 1 5 m B X

An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90 0 seconds The length L is measured by using a meter scale of least count 1mm and the value is 20 0 cm The error in the determination of g 2014 would be A 1 7 C 4 4 B 2 7 D 2 27

A wind powered generator converts wind energy into electric energy Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy For wind speed v the electrical power output will be proportional to A B V v2

Zero Marks 0 In all other cases 100 cells each of e m f 5V and internal resistance 12 are to be arranged so as to drive maximum current in a 25 resistance Each row is to contain equal number of cells The number of rows she de Langhe tradin

If vectors cos coti sinot jand cof B cos sin 2 the value of t at which they are orthogonal to each other is Re AIPMT 2015 1 t 0 2 t 3 t i sin are functions of time then TO 40 cof T 200 T

4 Relative error 8 The dimensions of solar constant energy falling on earth per second per unit area are 1 MOLOTO 3 ML T 2 MLT 4 MT

45 A physical quantity P is given by the relation If t denotes the time the dimensions P P of constant a are 1 T 3 IT 1 2 1 4 T

4 The potential energy u of a particle varies with A x X B distance x from a fixed origin as where A and B are constants The dimensions of A and B are respectively 1 ML52T L 2 MLT 2 L 3 L ML 2 T 2

A wave function expressing the displacement a as a function of position and time t is given as Pe QB Rt which of the following expression has dimension different from other A aR B PR C D QR

Two point dipoles of dipole moment p and p2 are at a distance x form each other and p P2 The force between the dipoles is 1 4P P2 A 4 o X 1 6P P2 x4 41 0 B D 1 3 P P2 4 X 1 8 P1P2 41EO 2013

A student performs an experiment to determine the Young s modulus of wire exactly 2 m long by Searle s method In a particular reading the student measures the extension in the length of the wire to be 0 8 mm with an uncertainty of 0 02 mm at a load of exactly 1 0 kg The student also measures the diameter of the wire to be 0 4 mm with an uncertainty of 0 04 mm Take g 10 m s exact The Young s modulus obtained from the reading is O 2 00 3 x 10 N m O 2 0 0 45 1011 N m O 2 00 2 x 10 N m O 2 0 0 05 x 10 N m

ns ol C Find dimensional formula of if where C capacity V Voltage V 3 M LT A 4 M L T A 1 M L T A 2 M L T A 1 C M L T A V M LT A M L T A 1

D 14 35 180 Ramesh joined the class XI by one week late He missed the concepts of units and measurements chapter in physics Teacher asked him a question for checking his knowledge of rule of significant figures Teacher gave to calculate the result of 9 0 1 7321 Ramesh told him that result contains two significant figures while another student Suresh said that result contains three significant figures Then Ramesh is right Suresh is wrong Suresh is right Ramesh is wrong Both are right Both are wrong Solution Answer 2 Hint Use significant rule of addition Sol 9 0 1 7321 10 7321 With correct significant rule result 10 7 Le result have three significant figures

Ans 0 9 0 023 micro farad A circuit is shown in the following figure for which C 3 0 011 F C 5 0 01 F and C3 1 0 01 F If C is the equivalent capacitance across AB then C is given by Options 1 2 144 C C C C C 0 9 0 114 F 0 9 0 01 F B

123 The velocity of water waves may depend on their wavelength 2 the density of water p and the acceleration due to gravity g The method of dimensions gives the relation between these quantities as A v k g p B v kg C v kg p where k is a dimensionless D v k 2 g p constant

16 If two jaw of vernier calliper are joined then vernier scale zero is on left of main scale zero and 4th vemier scale division coincides with a main scale division then find zero error If one division of main scale equals 1 mm and 10 vernier scale divisions equals 9 main scale divisions then 1 ve error of 0 4 mm 2 ve error of 0 4 mm 3 ve error of 0 6 mm 4 ve error of 0 6 mm 4 The 22 What show

Least count LC is the minimum length measured by a Vernier callipers and Let us define Vernier constant VC 1 MSD 1 VSD Each main Scale division MSD of the callipers is 1mm and N divisions of main scale are divided into 10 Vernier scale divisions VSD If N 6 find LC in mm

city 4 Thrust wance The period of oscillation of a simple pendulum in in rock an experiment is recorded as 2 63s 2 56s 2 42s 2 71s and 2 80s respectively The average absolute error is 1 0 1s The length breadth and thickm 2 0 11s 3 0 01s 4 1 0s

Calculate the moment of inertia of the shape about the indicated axis 5 00 30 00 15 00 17 50 17 50 5 00 1 y 2 10 00 3 5 00

In an experiment of simple pendulum the errors in the measurement of length of the pendulum L and time period 7 are 3 and 2 respectively The maximum percentage error in the value of T O 5 O 7 O 8 is

In transformer power of secondary coil is 1 less than primary coil 2 more than primary coil 3 more in step up and less in step down than primary coil 4 more in step down and less in step up than primary coil

In the figure shown battery I has em nal resistance 102 Battery 2 has emf 2V ar internal resistance 302 The wires have negligib resistance What is the potential difference acro the terminals of battery 2 1 4V IA 6V 12 ww 32 www b 2 2 1 5V

esistance ed in it gnitude 0 lio d b 2 5 mJ O 1 coil of inductance L 50 H and resistance 0 52 is connected to a battery of emf 5 V A resistance of 100 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 a 1 25mJ c 0 65 mJ d 0 12 mJ and F 0 present ABCDE a BL c 2E The se Cross as a L b d