Unit & Dimensions Questions and Answers

b x The dimensions of a b in the relation E 1 where at E is the energy x is the displacement and t is time are a ML T c ML T 2 b M L T d MLT 2 W

3 1When two resistors R and R are connected in parallel then their parallel combination is given by Rp R are AR and AR respectively then error in measurement of their parallel combination that is ARp is equal to R R R R 2 3 If error in measurement of R and 1 R AR AR R R2 AR AR R R 4 2 Rp 4 AR R AR AR R AR R R 6

In two COP at temp 10 C the number of beats are 5 If temp is made to 20 C the number of beats will be 1 less than 5 3 more than 5 2 equal to 5 4 Both 1 and 3

2 A steam power plant operates between a pressure of 6 MPa and 10 kPa Steam enters an isentropic turbine at 500 C Water enters the steam generator at 45 C at a rate of 200 kg s Determine a the cycle efficiency and b the rate of mass flow rate of condenser cooling water if the cooling water enters at 20 C and leaves at 32 C 10 4 plz Solve it in 20 mins I will thumb you up

A 2kg copper block is heated to 500 C and then it is placed on a large block of ice at 0 C If the specific heat capacity of copper is 400 J kg C and latent heat of fusion of water is 3 5 x 105 J kg the amount of ice that can melt is O 7 8 kg 7 5 kg O 8 7 kg

which lies in the same plane of a circular loop of conducting wire as shown in the figure Then A A no current will be induced in the loop the current induced in the loop will B change its direction as the charged particle passes by C the current induced will be anticlockwise D the current induced will be clockwise Feedback

les The pressure of confined air is p If the atmospheric pressure is P then 1 Pris equal to p 2 P is less than p 2 Y P is greater than p 4 P may be less or greater than p depending on the mass of the confined air

A 3 6 cage induction motor is connected through an auto transformer with a tapping of 70 which restricts the maximum line current drawn from a 415 V 3 6 supply to 130 A If the starting current is 5 times the full load current then the maximum permissible full load kVA of the motor will be

51 If a unit vector is represented by 0 51 0 81 0 then the value of c is 1 1 2 0 11 3 0 01 0 39 t 52 4 NI 0 25 0 6 0 25 0 64 0 89 The magnitude of vector AB and C respectively 12 5 and 13 units and A B Ct the angle between A and B is 1 0 At

When forces F F and F3 are acting on a particle of mass m such that F and F3 are mutually perpendicular then the particle remains stationary If the force F is now removed then the acceleration of the particle is 2 O F m

A light string passes over a frictionless pulley To one of its ends a mass of 6 kg is attached To its other end a mass of 10 kg is attached as shown in the figure What is the tension in the string Take g 10 m s O O 25 N 30 N 50 N 75 N 6 kg 10 kg

37 In the circuit shown in the figure if the po point A is taken to be zero the potential at point B is 1 Av 2 R 1 2 V R A4116 1 V 2 V 292 1AC 2A B 42 A AIPMT Mains 2011 2 1 V

A long cylindrical conductor of radius R has two cylindrical cavities of diameter R running parallel to its axis as shown in figure The conductor carries a uniform current density J The field strength B at position a HJR then find a 68 68 y Q x 2R along the x axis is P R

If dimensions of critical velocity v of a liquid flowing through a tube are expressed as n p r where and r are the coefficient of viscosity of liquid density of liquid and radius of the tube respectively then the values of x y and z are given by n Re AIPMT 2015 1 1 1 1 3 1 1 1 2 1 1 1 4 1 1 1 19

This section contains 1 Assertion Reason type question which has 4 choices A B C and D out of which ONLY ONE is correct A Dimensional formulas of work energy and torque are same R Two or more than two quantities can have same dimensional formula but the converse is not true Only One Correct Answer A Both A and R are true and R is the correct explanation of Al

of b a Figure 2 A thermodynamic system is taken from state a to state c in Figure 2 along either path abc or path adc Along path abc the work W done on the gas is 453 J Along path adc the work done on the gas is 123 J The internal energies of each of the four states shown in the figure are U 148 J U 241 J U 678 J and Ug 333 J Calculate the heat flow Q for each of the four processes ab bc ad and dc In each process does the system absorb or liberate heat Express the final answer here as the sum of the 4 Q values with zero digits of precision C d V

A 9 B 35 C 6 N D 9 If a wheel is rolling without slipping on a horizontal surface at a constant linear speed the the point of contact has A backward acceleration C an upward acceleration B zero acceleration D a downward acceleration

26 180 Mark for Review If energy E velocity V and time 7 are chosen as the fundamental quantities the dimensional formula of surface tension will be O E V T O EV T 02 49 hr min O EV T

As the temperature of a metallic resistor is increased then product of its resistivity and conductivity 1 Increases 2 Decreases 3 Remains constant 4 May increase or decrease 1 3 13 For

The entropy of any system is given by mathongo mathongo mathongo mathongo mathongo mathongo ukR S a 3ln mathongo mathongo mathongo JB2 3 mattongo mathongo mathongo mathongo mathongo mathongo mathongo mathongo mathonga where a and 3 are the constants J k and R are no of moles mechanical equivalent of heat Boltzmann constant and gas constant respectively mathongo mathongo mathongoma Take S do thongo mathongo mathongo T 4 a and k have the same dimensions mathongo mathongo mathongo mathongo mathongo mathongo mathongo Choose the incorrect option from the following ongo mathongo mathongo mathongo 1 a and J have the same dimensions matho math 2 S 3 k and uR have the same dimensions 3 S and a have different dimensions mathongo mathongo mathongo mathongo mathongo mathongo mathongo mathongo ame dimensions mathongo mathongo mathongo mathongo

A tuning fork of frequency 512 Hz makes 4 beats per second with the vibrating string of a piano The beat frequency decreases to 2 beats per sec when the tension in the piano string is slightly increased The frequency of the piano string before increasing the tension was AIPMT Prelims 2010 1 508 Hz 2 510 Hz 3 514 Hz

Three particles A B and Care situated at the vertices of an equilateral triangle of side length 3 m Each of the particles moves with constant speed 2 m s A always has its velocity along AB B along BC and C along CA After what time will the particles meet each other 1 s 2 s 1 5 s

A large parallel plate capacitor whose plates have an area of 1 m and are separated from each other by 1 mm and potential difference is being changed at a rate of 25 V s If the dielectric between the plates has the dielectric constant 10 then the displacement current at this instant is 0 22 A 11 A 2 2 A

The radius of a spherical body is 10 0 5 cm Then correct option is are 1 The percentage error in radius is 5 2 The percentage error in volume is 10 3 The percentage error in volume is 15 4 Both 1 3

the aircraft in 8 4 us Ans 4 2 x 10 new Express the number of seconds in a day and in a yea in orders of magnitude Ans 10 10 in the univers

5 How many of the atoms in Question 3 can fit within a spherical planet with a diameter of 2 X 104 km 3 The Moon is approximately 400 000 km from the Earth An atom of a certain element has a diameter of 4 X 108 cm Given 1 km 1 000 m and 1 m 100 cm about how many atoms of this element can be lined up between Earth and Moon

35 Which of the following is are unit of measurement of force kg x m iii dyne s 2 Only i ii iii 3 Only i i newton 1 Only i iii ii g x cm s 4 i ii iii iv

The distance moved by a particle in time t from centre of a ring under the influence of its gravity is given by x a sinct where a co are constants If oo is found to depend on the radius of the ring r its mass m and universal gravitational constant G Using dimensional analysis find an expression for o in terms of t m and G i found to depend upon UD0004

A number X which represents the age of the universe depends upon universal gravitational constant G speed of light c mass of electron m mass of proton m elementary charge e and permittivity of free space then taking Xoc em 2m the equation becomes 1 X e4 m m c G vd14 4 e m m c G 2 X 3 X m m c G 4 X m m c G P

t 8 If vector A coscti sinati and B cos 2 2 are functions of time then the value of t at which they ar orthogonal to each other is AIPMT 2015 a t I 2 c t 0 b t d t T IT i sin

mit the g dimensional formula for Force F pressure Pf and dimension of Lp if LB B v d sin unit mass length 2 where in the v velocity t time base

electrical circuit in terms of dimension of mass M of length L of time T and of current I would 2007 be a ML T c ML T 12 b ML T T d ML T 1 11

86 A ball is rolled off the edge of a horizontal table at a speed of 4 ms 1 It hits the ground after 0 4 s Which statement given below is true It hits the ground at a horizontal distance 1 6 m from the edge of the table b The speed with which it hits the ground is 4 0 ms c Height of the table 1m d It hits the ground at an angle of 60 to the horizontal roplane is flying at a constant height of 2 km towards

A physical quantity of the dimensions of length e that can be formed out of c G and is velocity of light G is universal gravitation and e is charge 71 2 e 4 a c 2 0 G e 1G 4 o C b d is c 4 constant of 2017 71 2 1 e G4TEO 71 2 e Game

3 mgh 4 mgh A large parallel plate capacitor whose plates 6 have an area of 1 m and are separated from each other by 1 mm is being charged at a rate of 25 V s If the dielectric between the plates has the dielectric constant 10 then the displacement current at this instant is 1 25 A 2 11 A 3 2 2 A 4 1 1 A 3 mgh 4 7mgh center foreraft co 1 m 1 mm 25 Vsafe fatif da ter 1 25 A 2 11 A 3 2 2 uA 4 1 1 A

3 6 2 cm 8 cm 4 9 cm 2 9 cm A body of mass m rises to height h R 5 from 5 the earth s surface where R is radius of earth the increase in gravitational potential energy is 1 mgh 2 mgh 4 mgh 5 3 mgh 3 6 2 cm 8 cm 4 9 cm 2 9 cm a f 1 mgh 5 3 mgh yeah R q graff 2 mgh 4 mgh

The formula P at distance x and time t The dimensional formula for a is relates power P 42 P 1 ML T 3 MLT 2 M LT 4 M L T a at 1 ML T 3 ML T t 1 2 MLT 4 ML T

1 The angle between vectors and is angle between vectors 35 and 26 is 8 71 6 KIN 5m The 11 1 a KIM 7n 6 H 6 4 1 3 KIN 5n 6

If time t energy E and momentum P taken as base quantities then dimension of mass m is 1 m ktP E 2 m kt p E 3 m ktoP E 1 4 m kt P 1E 1 divisions on vernier scale of vernier

SAMPLE PROBLEM 2 4 A particle moves in the xy plane so that its x and y coordinates vary with time according to x t At Bt and y t Ct2 D where A 1 00 m s B 32 0 m s C 5 0 m s and D 12 0 m Find the posi tion velocity and acceleration of the particle when t 3 s Solution The position is given by Eq 2 5 with the expressions given for x t and y t Substitute for A B C D and t then find out r as F Now x y At Bt i Ct D Result The velocity components are found from Eq 2 12 dx dt ax dy dt Substitute for A B C D and t then find out v as v vy The components of the acceleration are ay V x Vy dvx dt dvy dt Position vector r d dt d dt At Bt 3At B dt i d Ct D 2Ct dt At t 3 s the acceleration is Substitute for A B C and t then find out a as 3At B 6At 2Ct 2C i a a a m s i m s j

An electron of stationary hydrogen atom passes 20 fa un any scracia te I from the fifth energy level to the ground level The velocity that the atom acquired a result of 3 T WITH photon emission will be m is the mass of the atom R Rydberg constant and h Planck s constant 1 3 25m 24hR 24hR 25m 2 4 24m 25hR 25hR 24m 1 3 hifi R fearf sitt mea a 25m 24hR 24hR 25m 2 4 24m 25hR 25hR 24m

A ray of light travelling in the direction 31 41 incident on a plane mirror After reflection it travel along the direction 31 43 Then choose the correct statement s A Mirror is kept in x y plane B Normal of the mirror is along C Angle of incident is 37 D Mirror is kept in x z plane

Velocity A particle is moving along a circle such that it completes one revolution in 40 seconds In 2 minutes 20 seconds the ratio 1 O 2 3 7 2 7 displacement is distance R

3 If energy e density p and power P form a fundamental system of units the dimensional formula of momentum in terms of these quantities is a e7p P 3 c e7 5 p1 5 P 2 5 b e7 5 p 5 P 3 5 d e3 5 p 5 P 3 5

1 GN Z11 is the most distant galaxy we have observed its distance from us is 9 8 Giga parsecs Giga 109 The parsec symbol pc is a unit of length used to measure large distances to astronomical objects outside the Solar System If 1 pc 3 26 light years ly and 1 ly 9 45x1015 m a How far is GN z11 in ly b How far is GN z11 in km 2 The size of protons have been measured to be about 1 fm A femtometer symbol fm is 10 15 meters Compare the distance to GN z11 above to the size of a proton HINT First convert the two measurements to the same units and then take the ratio between the two I am looking for an answer telling me only the order of magnitude difference powers of ten 3 You use about 3 x 108 kg m s 2 of energy every day How much is that in kWh kilowatt hour HINT look at the lecture slides for help but show

The equation of trajectory of a projectile is given as 02 X The maximum height of projectile is y 2x 2 empe Symbols have usual meanings and Sl unit MAR WOY 1 4 mt mont bei elitos 2 1 m 3 2 me sub noite 4 10 m SY

5 Time intervals measured by a clock give the following readings 1 25 s 1 24 s 1 27 s 1 21 s and 1 28 s What is the percentage relative error of the observations 1 4 3 1 6 2 16 4 2

Find error in acceleration due to gravity of time period for 100 oscillations is 80 secon ds measured with wrist watch of least cou nt of 1 second and length of pendulum is 5 cm

velocity The dimensional formula of AB is b ML T a ML T If A f X B x are a MOLTO c ML T d M L T0 where x represents position and A and B are unknown quantities then dimensions of b MOLOTO c MOL T 1010 G d ML T

The kinetic energy of a particle varies according to relation K velocity The dimensional formula of AB is a ML T b ML T c MIST B x Here x is the distance and v is the d M 13701