Unit & Dimensions Questions and Answers

pl I and area of cross secion a is given by R a where p is the electrical resistivity What is the dimensional formula for electrical conductivity o which is the reciprocal of resistivity AIEEE 2012 Online 1 M 1 L 3 T3 A 3 M 21 3T2A 1 2 ML T 3A 4 MI 3T 3A 2

A particle is dropped from height Initially a constant horizontal velocity is given to the particle Taking g to be constant everywhere variation in kinetic energy of particle with time t is correctly shown in KE 2 KE KE KE m

A deep rectangular pond of surface area A containing water density p specific heat capacity s is located in a region where the outside air temperature is at a steady value of 26 C The thickness of the frozen ice layer in this pond at a certain instant is x NEET 2019 Odisha Taking the thermal conductivity of ice as K and its specific latent heat of fusion as L the rate of increase of the thickness of ice layer at this instant would be given by 1 26K px L 4s 3 26K px L 2 26K px L 4s 4 26K pxL

PROBLEM 4 19 FIG 4 21 A rectangular field of 0 54 hectare is represented on a map by a rectangle of 3 cm x 2 cm Calculate the R F Draw a diagonal scale to read up to a single metre and that is long enough to measure up to 600 m

A very long open cylindrical container of radius R 5m has two small holes at the bottom Initially the holes are closed and water is filled into the container Now the container is rotated about its axis with an angular velocity w 12rad sec As seen from the rotating frame of the container The initial velocity of efflux after opening the holes will be g 10m s h 5m 3 h 3 R

The base of a solid is the region between the curve y p x x 3px 0 x 3p y 20 and the X axis If the cross sections perpendicular to the x axis are equilateral triangles with ba running from the x axis to the given curve find the volume of the solid obtaine

ea of the c 5 25 cm 5 4 cm error is 11 Young s modulus of steel is 1 9 x 10 1 N m2 When m expressed in cgs units of dynes cm2 it will be equal 2 antities to 1 N 105 dyne 1 m 10 cm a 1 9 x 1010 c 1 9 x 10 2 b 1 9 x 10 1 d 1 9 x 10

2 A quantity X is given by col AV AT where E is the permittivity of the 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

8 If the energy E Ghe where G is the universal gravitational constant h is the Planck s constant and c is the velocity of light then the values of p q and r are respectively a 1 2 1 2 and 5 2 c 1 2 1 2 and 3 2 b 1 2 1 2 and 5 2 d 1 2 1 2 and 3 2

17 A famous relation in physics with many printing errors relates the moving mass m with rest mass for a moving object with n speed v is printed as m 1 b c The dimensional formula of no and b are respectively c is speed of light

Using Bohr s formula for energy quantization the ionisation potential of the ground state of Li atoms is 2 13 6 V 4 10 2 V 1 122 V 3 3 4 V The total energy of an electron in the hydroge The kine

23 In the following circuit the output Y becomes 1 for the inputs A B C i ii a A 1 B 0 C 0 b A 0 B 1 C 1 c A 0 B 0 C 0 d A 1 B 1 C 0 iii Y

In C G S system the magnitutde of the force is 100 dynes In another system where the fundamental physical quantities are kilogram metre and minute the magnitude of the force is 1 0 036 2 0 36 3 3 6 4 36

mg 3 2K 32 The time period of spring block system is T The spring is cut into two parts with their length in ratio of 2 3 Find the time period of oscillation of same block with longer part of spring 1 2 K 3m 3 25K 2 2 5m 3K 12m 4 2 5K m ir placed at lowest point of 37

A uniform metal disc of radius R is taken and out of R it a disc of diameter is cut off from the end The 2 centre of mass of the remaining part will be R 10 from the centre 2 R 3 from the centre 4 R 15 R from the centre from the centre

45 45 A wave function expressing the displacement y as a function of its position x and time t is given as y F log Qx e Rt Which of the following expressions has dimensions different from other yR PR

Pre Medical A particle is acted upon by a force of magnitude which is always perpendicular to the velocity of the particle The motion of the particle takes place in a plane It follows that 1 its velocity is constant 2 its K E is constant 3 its acceleration is constant 4 it moves in a straight line 58 9

Suppose a quantity x can be dimensionally represented in terms of M L and T that is x M LbTc The quantity mass a Can always be dimensionally represented in terms of L T and x b Can never be dimensionally represented in terms of L T and x c May be represented in terms of L T and x if a 0 d May be represented in terms of L T and x if a 0

The frequency of vibration f of a mass m suspended from a spring of spring constant K is given by a relation of this type f Cm K where C is a dimensionless quantity The value of x andy are 1 z 1 y 1 2 x 1 2 Y 4 x 3 x 1 y 2 1 22 16 2

If the unit of velocity is 4ms the unit of acceleration is 24ms 2 and the unit of force is 6 newtons then choose the CORRECT statements Unit of energy is 4 joule Unit of momentum is 1NS Unit of power is 24 watt Unit of momentum is 2 3Ns

The count rate for 10 gm of radioactive material was measured at different times and this has been shown in the graph with scale given The half life of the material and the total count in the first half value period respectively are 1 Count rate per minute 2 100 75 50 25 55 12 5 Question Type Single Correct Type 0 1 2 3 4 5 6 7 8 9 10 Time in hours 4 hour and 9000 approximately 3 hour and 14100 approximately

Considering Force F Velocity V and Energy E as fundamental quantities match the correct dimensions of following quantitie List II P Q R ERA S Mass List I Light year Frequency Pressure F O P1 Q2 R3 S 4 P 4 Q 1 R 2 S 3 P 4 Q 1 R 3 S 2 P 3 Q 1 R 4 S 2 F VE 2 F V E F V E F V E 3 F

4 An electron accelerated through a potential difference of V volt collides with a hydrogen atom in the ground state Identify the correct statement related to the elastically e of collision a e 1 for any value of V b e 1 for any value of V

1 The least count of a stop watch is seconds What is the percentage error in the measurement of time 5 3 second The time of 20 oscillations of a pendulum is measured to

Ramesh goes to a children park near his house The park is of square shape whose side length is a 10 0 0 1 m The area of this park is 1 100 2 m 3 10 0 2 m 2 100 0 0 2 m 4 100 0 0 1 m There are some measured data as A 4 00 m B 4 000 m C 1 0000 m and D 2 0 m then 1 A is most precise 2 B is most precise 3 C is most precise 4 D is most precise

Which of the following pairs does not have same dimensional formula 1 Work and torque 2 Angular impulse and Planck s constant 3 Strain and Poisson s ratio 4 Surface tension and stress The coefficient of thermal conductivity have dimensional formula 1 M L T 1K 3 M L 1 T 1 K 2 M L 1 T 3 K 4 MLT 3 K 1

a Increases with time c Independent of time b Decreases with time d None of these A person moves 30 m north and then 20 m towards east and finally 30 2 m in south west direction The displacement of the person from the origin will be J K CET 2004 a 10 m along north c 10 m along west b 10 m long south d Zero An aeroplane flies 400 m north and 300 m south and then flies 1200 m upwards then net displacement is KCET 1999 JIDMER 1000 DO SO Am

The refractive index of water tion real depth apparent depth rela is found to have values of 1 34 1 38 1 32 and 1 36 the mean value of refrac tive index with percentage error 1 1 35 1 48 3 1 36 6 2 1 35 0 4 1 36 0

Q19 A rocket with a lift off mass 3 5 x 10 kg is blast upward with an initial acceleration of 10 m s2 Then the initial thrust of the blast is a 1 75 x 105 N b 3 5 105 N c 7 0 x 105 N d 14 0 x 105 N

180 If e Eo h and C respectively represents electronic change permittivity of free space e EphC planks constant and speed of light then has the dimensions of A angle C strain 1 A B 3 A B C B relative density D current 2 D 4 A B C D

ne nd ing is e 3 4 1 us A current I flows through a uniform wire of diameter d when the electron drift velocity is v The same current will flow through a wire of diameter d 2 made of the same material if the drift velocity of the electrons is 4 1 4 1 v 4 3 2v 2 v 2 4 4v Z NODE02 BOAH A DENIT FLEV02

Example 7 An air bubble starts rising from the bottom of a lake Its diameter is 3 6 mm at the bottom and 4 mm at the surface The depth of the lake is 250 cm and the temperature at the surface is 40 C What is the temperature at the bottom of the lake Given atmospheric pressure 76 cm of Hg and g 980 cm s Solution At the bottom of the lake volume of the bubble

If L Q R represent inductance charge and resistance respectively the units of This question includes concepts from 12th syllabus 1 will be those of current QR L 2 will be those of energy QL 3 will be those of current R Q R Q R L 4 will be those of power

Using the expression 2d sin 0 one calculates the values of d by measuring the corresponding angles 0 in the range 0 to 90 The wavelength is exactly known and the error in 0 is constant for all values of 0 As 0 increases from 0 1 The absolute error in d remains constant 2 The absolute error in d increases 3 The fractional error in d remains constant pribrisque at eenevinu srit Jedi beveils 4 The fractional error in d decreases

If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as n Xpr where np and r are the coefficent of viscocity of liquid density of liquid and radius of the tube respectively then the values of x y and z are given by 1 1 1 1 2 1 1 1 3 1 1 1 A 1 1 1

A car of mass m is moving on a level circular track of radius R If s represents the static friction between the road and tyres of the car the maximum speed of the car in circular motion is given by A B C mRg s VHs Rg VHs mRg

A charge of 2C is placed on the x axis at 1m from the origin along ve x axis Infinite number of charges each of magnitude 2C are placed on x axis at 1m 2m 4m from origin along ve x axis The first charge is positive and alternate charges are of opposite in nature The electric field intensity at the origin is

The period of a body under SHM is presented by T PaDbSc where P is pressure D is density and S is surface tension The value of a b and c are 1 3 1 2 2 1 3 1 2 9 4 1 2 9 2 3 1 1 3 1 2 2 1 3

AT 0 01 0 06 0 20 0 09 0 18 s 5 0 54 s 5 0 11 s mean That means the period of oscillation of the simple pendulum is 2 62 0 11 s i e it lies between 2 62 0 11 s and 2 62 0 11 s or between 2 73 s and 2 51 s As the arithmetic mean of all the absolute errors is 0 11 s there is already an error in the tenth of a second Hence there is no point in giving the period to a hundredth A more correct way will be to write

If the constant of gravitation G Planck s constant h and the velocity of light c be chosen as fundamental units then find the dimensions of the radius of gyration

The diameter of a sphere is 2 14 cm Calculate the volume of the sphere to the correct number of significant figures

What equal charges should to be placed on earth and moon to neutralize their gravitationa attraction mass of earth 1025 kg mass of moo 1023 kg 1 8 6 10 3 C 3 8 6 10 C 2 6 8 x 1026 C 4 9 106 C

r4 then the 8nl dimensions of n by taking velocity v time T and mass M as fundamental units are If discharge rate is given by V where V rate of flow of volume P pressure difference r radius l length of tube Question Type Single Correct Type 1 M vT 2 2 Mv T 2 3 MvT 2

1 The relation between velocity and time of body is given B v A Ct the units of A B and C will be 2 3 1 A A m B m s C m s D m s B m s A m m s m s In terms of the seven fundamental SI units in the MKS system the Ohm is written as where symbols have usual meaning IS 0 kg m A s kg m s C dimensions of C m s m s m s4 m s B C D Of the following quantities which one has dimensions different from the remaining three A Energy per unit volume B Force per unit area C Product of voltage and charge per unit volume D Angular momentum per unit mass EJ 502 kg m C S E m J and G denote energy mass angular momentum and gravitational constant respectively Then the are kg m A S

2 Let A A A A A A A be a regular hexagon Write the x components of the vectors represented by the six sides taken in order Use the fact that the resultant of these six vectors is zero to prove that coso cost 3 cos2 3 cos3 3 os4 3 os5 3 0 Use the known cosine values to verify the result A6 A5 A A4 A3 60 A2 Figure 2 E2

A star moves away from earth at speed 0 8 c while emitting light of frequency 6 10 4 Hz What frequency will be observed on the earth c speed of light 1 0 24 10 4 Hz 2 1 2 x 10 4 Hz 3 2 10 4 Hz 4 150 10 4 Hz 0 8 x 6x

Application of 46 If the buoyant force F acting on an object depends on its volume V immersed in a liquid the density p of the liquid and the acceleration due to gravity g The correct expression for F can be 1 Vp g 3 2012 pg V 4 pgv 2

N 44 1 1 1 1 1 2 3 2 1 A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity n After some time the velocity of the ball attains a constant value known as terminal velocity VT The terminal velocity depends on i the mass of the ball m ii n iii r and iv acceleration due to gravity g Which of the following relations is dimensionally correct Mora Pinroli Read Sikar Rajasthan Ph 01572 255500 1 40

A lift starts from the top of a mine shaft and descends with a constant speed of 10 m s 4 s later a boy throws a stone vertically upwards from the top of the shaft with a speed of 30 m s If stone hits the lift at a distance x below the shaft write the value of Given value of 20 6 491 X 3 in m Take g 10 m s

d The dimension of a derived quantity is never zero in any base quantity 10 If unit of length and time is doubled the numerical value of g acceleration due to gravity will be a doubled b halved sono c four times minulov v toit 922 d same asasi 11 Using mass M length L time T and current A as fundamental quantities the dimension More than 1 The dimensions of Identify the pair s a Torque and worl Vou