Kilo watt hour is the unit of

1) Power

2) Energy

3) Pressure

4) Time

1 Horse power is equal to

1)746 W

2) 746 J

3)1746 W

4)373 W

Pascal is the S.I. unit of

1) Impulse

2) Coefficient of Viscosity

3) Surface Tension

4) Modulus of elasticity

In the following which is not the unit of time

1) Lear year

2) Lunar month

3) Light year

4) sidereal year

Candela is the SI unit of

1) Intensity of sound

2) Luminous intensity

3 )Intensity of Electric field

4) Luminous Flux

kg m s ^{-1} is the unit of

1) Force

2) Linear momentum

3 ) Angular momentum

4) Torque

Unit used to measure nuclear diameters is

1) fermi

2) angstrom

3) micron

4) nanometre

Parsec is the unit to measure

1) Time

2) Distance

3) Impulse

4) Moment of inertia

1 kWH is equal to

1) 36 kJ

2) 36 x 10^{-5} J

3) 360 J

4) 36 x 10^{5} J

If n Ns = 1g cm/s then the value of n is

1)10^{5}

2) 10^{-5}

3) 10^{-6}

4) 10^{-7}

The dimensional formula of a pseudo force is

1) M^{0}L^{0}T^{-1}

2) M^{0}L^{0}T^{0}

3) M^{ 0}L T^{0}

4) MLT^{-2}

Physical quantity having the unit J kg ^{-1 }is

1) Thermal capacity

2) Specific Heat

3) Latent heat

4) Heat

1 fermi is equal to

10^{-7} micron

2) 10^{-5} angstrom unit

3) 10^{-3} nanometer

4) none of the above

If P is X-ray unit and Q is micron, thenP/Q=

1)10^{7}

2)10^{-7}

3) 10^{5}

4) 10^{-3}

Unit of magnetic induction field B is

1) tesla

2) Wb m^{-2}

3) N (Am) ^{-1 }

4) all the above

S.I. unit of Electric intensity is

1) Hm^{-1}

2) Nm^{-1}

3) Vm^{-1}

4)NC

17. Which of the following is expressed correctly

1) Magnetic permeability —>Fm-1

2) Permittivity —>Hm-1

3) Relative permittivity -> Vm-1

4) Intensity of Magnetizing field —> Am-1

8 Which of the following is not expressed correctly with respect to units ?

1) Specific heat ->J kg-1K-1

2) Entropy ->Jk-1

3) Thermal capacity—>Jkg-1

4) Temperature gradient —>m-1k

19. SI unit of Stefan’s constant is

1)w m^{-2} K^{-4}

2) J m^{-2}K^{-4}

3)W m^{-1} K^{-1}

4) W m^{-2} K^{-2}

20. SI unit of Thermal resistance is

Wk^{-1}

2)W^{-1}k

3)W^{-1}k^{-1}

4) Wm^{-1}k^{-1}

21. If the units of length, mass and time are doubled, the unit of force will be

1) doubled

2) halved

3) quadrupled

4) unchanged

22. If U_{1} and U_{2} are the units of a physical quantity and n_{1} and n_{2} are its numerical values, then

_{1}) n_{1}/n_{2}=U_{1}/U_{2}

_{2})n_{1}/n_{2}= \sqrt { \frac { U_{1} }{ U_{2} } }

3) (n_{1}/n_{2})^{2}= U_{1}/U_{2}

4)n_{1}/n_{2}=U_{2}/U_{1}

23. A and B are the numerical values of a physical quantity and C and D are its units in two systems of measurement. If C > D, then

1)A>B

2)A** 3)A = B 4) A & B cannot be related
24. Derived unit is **

1)candela

2)steradian

3) ampere

4) volt

25. The set of quantities which cannot form a group of fundamental quantities in any system of measurement is

1) Length, Mass and Time

2) Length, Mass and velocity

3) Mass, time and velocity

4) Length, Time and velocity

26 The set of quantities which can form a group of fundamental quantities in any system of measurement is

1) Velocity, Acceleration and Force

2) Energy, Velocity and Time

3) Force, Power and Time

4) all the above

27. The fundamental unit which is common in COS and SI is

1) metre

2) gram

3) second

4) all the above

28. The fundamental quantity which is common in MKS and SI is

1) Length

2) Mass

3) Time

4) all the above

29. J kg^{ -1} K^{ -1} is the unit of

1) Boltzmann constant

2) PLANCK’S constant

3) Gas constant

4) all the above

30. The ratio of SI unit to CGS unit of Planck’s constant is

1) 10^{ 7}

2) 10^{– 7 }

3) 10^{ 3 }

4) 10^{ 5}

A) Work and energy have the same units in any given system of measurement

B) Work and power have the same ratio of SI unit to CG.S unit

1) Statement A is true and B is false

2) Statement A is false and B is true

3) Both A and B are true

4) Both A and B are false

S = A(1–e ^{ -Bxt}) where S is speed and ‘x’ is displacement. Then unit of B is

1)m^{ -1} s^{ -1}

2) m^{ -2} s

3)s^{ -2}

4) s^{ -1}

A standard unit should be

a) Consistent

b) reproducible

c) invariable

d) easily available for usage

1) Only a& b are true

2) Only a& c are true

3) Only a,c &d are true

4) a, b, c, d are true

The S.I unit of Moment of Inertia is

1) Kg/m2

2) Kg m2

3) N/m2

4)Nm2

The correct order in which the ratio of SI unit to CGS unit increases is

a) Power

b) Surface tension

c) Pressure

d) Force

1) c, b, d, a

2) c, a, b, d

3) d, a, b, c

4) a, c, d, b

Write the ascending order of the units of length given below.?

a) Fermi

b) Micron

c) Angstrom

d) Nanometre

1) a, b, d, c

2) a, c, d, b

3) a, c, b, d

4) a, b, c, d

Steradian is the solid angle subtended at the centre of the sphere by its surface whose area is equal to __ of the sphere.

1) the radius

2) square of the radius

3) cube of the radius

4) reciprocal of the radius

If E, M, J and G respectively denote energy, mass, angular momentum and universal gravitational constant.

The quantity which has the same dimensions as the dimensions of EJ2/M5 G2

1)time

2) angle

3) mass

4) length

Dimensional formula of coefficient of viscosity is

1) ML^{-1}T

2) ML^{-1}T^{-1 }

3) MLT^{-1}

4) M^{-1}L^{-1}T

Dimensional formula of Intensity of Magnetization is

1)IL

2)IL^{-2 }

3)IL^{-1}

4) I^{-1}L

ML ^{-1}T^{-2} is the dimensional formula of

1) Modulus of Elasticity

2) Stress

3) pressure

4) All the above

The dimensional formula of the physical quantity whose S.I. unit is farad is

1) ML^{2} T^{-3} I2

2) M^{-1} L^{-3} T^{4} I^{2}

3) M^{-1}L^{-2}T^{4}I^{2}

4) M^{-1}L^{-2}T^{-3}I^{2}

The dimensional formula of the physical quantity whose S.I. unit is Hnv1 is

1) ML^{2} T^{-2} I^{2}

2) M L T^{-2}I^{-2 }

3) M^{2} L^{2} T^{-2}I^{-2}

4) ML T^{2}I^{2}

Heat and Thermal capacity differ in the dimensions of

1)Mass

2) length

3) Time

4) Temperature

45. Force constant and surface tension have the same dimensions in

1)Mass

2) length

3) Time

All the above

46. Boltzmann constant and Planck’s constant differ in the dimensions of

1) Mass and Time

2) Length and Time

3) Length and Mass

4) Time and Temperature

47. The pair of physical quantities having the same dimensions is

1) Power and Torque

2) Thermal capacity and specific heat

3) Latent heat and gravitational potential

4) Angular momentum and Impulse

48. A scalar quantity and a vector quantity having the same dimensions are

1) Gravitational potential and latent heat

2) Force and Tension

3) Specific heat and gas constant

4) Frequency and velocity gradient

49. The pair of scalar quantities having the same dimensions is

1) Moment of force and Torque

2) Angular velocity and velocity gradient

3) Thermal capacity and Entropy

4) Planck’s constant and Angular momentum

50. The pair of vector quantities having the same dimensions is

1) Force and Impulse

2) Moment of inertia and Moment of the couple

3) Surface Tension and Force constant

4) Thrust and weight

51. Quantity having units but no dimensions is

1) Intensity of sound

2) Solid angle

3) Strain

4) Relative density

52. Intensity of Magnetization has the same dimensions as

1) Magnetic susceptibility

2) Magnetic moment

3) Intensity of magnetizing field

4) Magnetic permeability

53. Dimensionless quantity is

1) Intensity level of sound

2) Magnetic susceptibility

3) Refractive Index

4) all the above

54. The pair of quantities having neither units nor dimensions is

1) Plane angle and specific gravity

2) Magnetic permeability and Relative permittivity

3) Coefficient of friction and coefficient of restitution

4) Linear momentum and Angular momentum

55. Dielectric constant has the same dimensions as

1) Stress

2) Strain

3) Electric capacity

4) Electric permittivity

56. If G is the universal gravitational constant, M is the mass, R is the radius and h is the altitude, then

\sqrt { \frac { GM }{ (R+h) } } has the dimensions of

1) Velocity

2) Potential energy

3) Force

4) Acceleration

(x^{2}/mass) has the dimensions of kinetic energy.

Then x has the dimensions of

1) Pressure

2) Torque

3) Moment of Inertia

4) Impulse

The quantity having negative dimensions in mass is

1) Gravitational Potential

2) Gravitational constant

3) Acceleration due to gravity

4) None of the above

The quantity having dimensions only in Temperature is

1) Latent heat

2) Entropy

3) Specific heat

4) Coefficient of linear expansion

The dimensional formula of Areal velocity is

1)M^{0}L^{2}T

2)M^{0}L^{2}T^{-1}

3) M^{0} L^{3}T^{-1}

4) M^{0} L T^{-2}

The dimensions of electric current in electric conductivity are

1)1

2) 2

3) 3

4)-2

Choose the false statement

1) relative permittivity is a dimensionless constant

2) Angular displacement has neither units nor dimensions

3) Refractive index is dimensionless variable

4) Permeability of vacuum is a dimensional constant

The pair of quantities having same units and dimensions is

1) Focal power and Magnifying power

2) Tension and surface Tension

3) Force and Electromotive force

4) power and electric power

h d G has the dimensions of (h = height, d = density, G = gravitational constant)

1) Pressure

2) Power

3) Torque

4) Acceleration

65. ( he/4π m )has the same dimensions as (h= Planck’s constant, e = charge, m = mass,)

1) Magnetic moment

2) Magnetic induction

3) Angular momentum

4) Pole strength

66. (M/Vr) has the dimensions of (M = Magnetic moment, V = Velocity, r = radius)

1) Pole strength

2) Electric charge

3) Electric potential

4) Force

67. If R is the Rydberg constant, C is the velocity and h is the Planck’s constant, then RCh has the dimensions of

1) Power

2) Angular frequency

3) Wavelength

4) Energy

68. If x times momentum is work, then the dimensions of x are

1) LT^{-1 }

2) L^{-1}T

3) ML^{-1}T^{-1}

4) MLT

Choose the correct statement :

1) The proportionality constant in an equation can be obtained by dimensional analysis

2) The equation V = u+at can be derived by dimensional method

3) The equation y = A sin wt cannot be derived by dimensional method

4) The equation \eta =\frac { A }{ B } { e }^{ -Bt } can be derived with dimensional analysis

The product of Energy and Moment of Inertia has the dimensions same as

1 ) the square of linear momentum

2) the square of angular momentum

3) angular impulse

4) Planck’s constant

The dimensional formula of magnetic induction is

1) MT^{-1}A^{-1}

2) MT^{-2}A^{-1}

3) MTA^{-2}

4) MT^{-2}A

The physical quantity which has dimensional formula as that of Energy/ mass x length is

1) Force

2) Power

3) Pressure

4) Acceleration

The SI unit of Moment of Inertia is

1)kg/m^{2 }

2)kgm^{2}

3) N/m^{2}

4) Nm^{2}

Dimensional formula of capacitance is

1) M^{-1}L^{-2}T^{-4}I^{2}

2) M^{-1}L^{-2}T^{4}I^{2}

3) ML^{2}T^{-4}I^{2}

4) ML^{-2}T^{4}I^{-2}

The modulus of elasticity is dimensionally equivalent to

1 ) Stress

2) Surface tension

3 ) Strain

4) Coefficient of viscosity

SI unit and CGS unit of certain quantity vary by 10^{3} times. That quantity is

1 ) Boltzmann constant

2) Gravitational constant

3) Planck’s constant

4) Angular momentum

The pair of physical quantities having the same dimensional formula are

1 ) Momentum, impulse

2) Momentum, energy

3) Energy, pressure

4) Force, power

A pair of physical quantities having the same dimensional formula is

1) Force and work

2) Work and energy

3) Force and torque

4) Work and power

The pair of physical quantities having the same dimensional formula

1) Angular momentum and torque

2) Torque and entropy

3) Power and angular momentum

4) None

The SI unit of magnetic flux is

1)Wb/m^{2 }

2) Am^{2}

3) Oersted

4) Weber

Planck’s constant has the same dimensions as

1) Energy

2) Power

3) Linear momentum

4) Angular momentum

How many ergs are there in one kilowatt – hour ?

1) 3.6 x 10^{ 6 }

2) 3.6 x 10^{10 }

3) 3.6 x 10^{13 }

4) 3.6 x 10^{11}

83. The unit of angular momentum in CGS system

1)Js

2) erg s

3) erg s ^{-1 }

4) cal s^{-1}

84. The fundamental unit which has the same power in the dimensional formula of surface tension and viscosity is

1)mass

2) length

3) time

4) none

85. The dimensions of Thermal resistance is

1) M^{-1}L^{-2}T^{3}K^{1 }

2) M^{0}L^{0}T^{-2}

3) MLT^{4}

4) MLT^{-1}

86. The dimensional formula of velocity gradient is

1) M^{0}L^{0}T^{-1}

2) MLT^{-1}

3) ML^{0}T^{-1 }

4) M^{0}LT^{-2}

87. Temperature can be expressed as derived quantity in terms of any of the following

1) Length and mass

2) Mass and time

3) Length, mass and time

4) In terms of none of these

88. The dimensional formula of coefficient of kinematic viscosity is

1) M^{0}L^{-1}T^{-1 }

2) M^{0}L^{2}T^{-1}

3) ML^{2}T^{-1 }

4) ML^{-1}T^{-1}

89. The fundamental physical quantities that have same dimensions in the dimensional formulae of torque and angular momentum are

1) mass, time

2) time, length

3) mass, length

4) time, mole

90. The dimensional formula for latent heat is

1) MLT^{-2}

2) ML^{2}T^{-2}

3) M^{0}L^{2}T^{-2}

4) MLT^{-1}

91. ML^{-1}T^{-2} represents

1) Stress

2) Young’s modulus

3) Pressure

4) All the above

92. Dimensional formula for angular momentum is

1) ML^{2}T^{-1}

2) ML^{3}T^{-1}

3) MLT^{-1}

4) ML^{3}T^{-2}

93. The physical quantity that has no dimensions is

1) Angular velocity

2) Linear momentum

3) Angular momentum

4) Strain

94. The energy density and pressure have

1) Same dimensions

2) Different dimensions

3) No dimensions

4) None

95. The dimensional formula ML^{2}T^{-2} represents

1) Moment of a force

2) Force

3) Acceleration

4) Momentum

96. The pair of physical quantities not having the same dimensional formula is

1) Acceleration, gravitational field strength

2) Torque, angular momentum

3) Pressure, modulus of elasticity

4) All the above

The dimensional formula for Torque is

1) M^{2}LT^{-2 }

2) ML^{2}T^{-2 }

3) M^{-1}L^{2}T^{-2}

4) MLT^{-2}

98. The dimensional formula for angular velocity is

1) M^{-1}LT^{-2}

2)M^{0}L^{-1}T^{0}

3) M^{-1}L^{-1}T^{0}

4) M^{0}L^{0}T^{-1}

Solar constant and Stefan’s constant have same dimensions in

1)Mass

2) Length

3) Time

4) All the above

The physical quantities not having same dimensions are

1) torque and work

2) momentum and Planck’s constant

3) stress and Young’s modulus

4) speed and (μ_{0} ε_{0}) ^{-1/2}

Out of the following the correct order of dimensions of mass increases is

a) Velocity

b) Power

c) Gravitational Constant

1) a, b, c

2) c, a, b

3) a, c, b

4) b, c, a

The correct order in which the dimensions of time decreases in the following physical quantities.

a) Power

b) Modulus of elasticity

c) Moment of inertia

d) Angular momentum

1)a, b, d, e

2) c, d, a, b

3) a, c, d, b

4) c, d, b, a

103. The time of oscillation of a small drop of liquid under surface tension depends upon density and surface tension s, as T ∝ p^{a} s^{b} r^{c}, then the descending order of a, b and c is

1)a>b>c

2)a>c>b

3)b>a>c

4)c>a>b

Which of the following is the most precise device for measuring length.

1) a vernier callipers with 20 divisions on the sliding scale

2) a screw gauge of pitch 1 mm and 100 divisions on the circular scale

3) an optical instrument that can measure length to within a wavelength of light

4) all the above

105. The time period of a seconds pendulum is measured repeatedly for three times by two stop watches A, B. If the readings are as follows

S.No. A — B

1. 2.01 sec — 2.56 sec

2. 2.10 sec — 2.55 sec

3. 1.98 sec — 2.57 sec

1) A is more accurate but B is more precise

2) B is more accurate but A is more precise

3) A,B are equally precise

4) A,B are equally accurate

106. Fundamental unit out of the following is

1) ampere

2) newton

3) ohm

4) weber

107 . The ratio of SI unit to CGS unit of a physical constant is 10 ^{ 7}. That constant is

1) Universal gas constant

2) Universal gravitational constant

3) Magnetic induction

4) Planck’s constant

108. Electron volt is the unit of

1) Power

2) Potential

3) Electron charge

4) Energy

109. The unit of reduction factor of tangent galvanometer

1) Ampere

2) Gauss

3) Radian

4) None

110. The SI unit of magnetic permeability is

1) Am^{ -1 }

2) Am^{ -2}

3) Hm^{ -1}

4)Hm^{ -2}

111. ML^{ 2} T^{ 2} I^{ -2 } is the dimensional formula for

1) Self inductance

2) Magnetic induction

3) Magnetic moment

4) Electric conductance

112. Magnetic induction and magnetic flux differ in the dimensions of

1) Mass

2) Electric current

3) length

4) Time

113. Electromotive force and Electric potential differ in the dimensions of

1) Mass

2) Length

3) Electric current

4) none of the above

114. Let ε _{0} denote the dimensional formula of the permittivity of vacuum. If M – mass L = length, T – time and A = electric current, then

1) ε _{ 0} =M^{ -1} L^{ 2} T^{ -1} A

2) ε _{ 0} =M^{ -1} L^{ -3} T^{ 2} A

3) ε _{ 0} =M^{ -1} L^{ -3} T^{ 4} A^{ 2}

4) ε _{ 0} =M^{ -1} L^{ 2} T^{ -1} A^{ -2}

115. Which of the following pairs is related as in work and force ?

1 ) Electric potential and Electric intensity

2) Momentum and velocity

3) Impulse and force

4) Resistance and voltage

116. The dimensional equation for magnetic flux is

1) ML^{ 2} T^{ 2} I^{ -1 }

2) ML^{ 2} T^{ -2 } I^{ -2}

3) ML^{-2}T^{-2}I^{-1 4) ML– 2 T -2 I-2
The units and dimensions of impedance in terms of charge Q are }

1) mho, ML^{ 2} T^{ -2} Q^{ -2}

2) ohm, ML^{ 2} T^{ -1} Q^{ -2 }

3) ohm, ML^{ 2} T^{ -2} Q ^{ -1}

4) ohm, MLT^{-1}Q^{-1}

118. The dimensional formula of 1/2 ε_{0} E ^{2} is (epsilon _{o }permittivity of free space and E electric field intensity)

1) ML^{ 2} T^{ -2}

2) MLT^{ -2 }

3) ML^{ -1} T^{ 2}

4) ML ^{ 2} T^{ -1}

119. Using mass (M), length (L), time (T) and electric current (A) as fundamental quantities the dimensions of permittivity will be

1) MLT^{ -1} A^{ -1 }

2) MLT^{ -2} A^{ -2 }

3) M^{ -1} T^{ -3} T^{ +4} A^{ 2}

4) M^{ 2} L^{ -2} T^{ -2} A^{ 2}

120. Dimensions of (1/με_{ 0},where symbols have their usual meaning are

1) L^{ -1} T

2) L^{ 2} T^{ 2}

3) L^{ 2} T^{ -2}

4)LT^{-1}

121. The correct order in which the dimensions of ‘Length’ increases in the following physical quantities is

a) Permittivity

b) Resistance

c) Magnetic permeability

d) Stress

1)a, b, c, d

2)d, c, b, a

3) a, d, c. b

4) c, b, d, a

122. (A): Plane angle has unit but no dimensional formula

(B): All dimension less quantities are unit less

1)Both A&B are true

3) Only A is true

2) Both A & B are false

4) Only B is true

123. Out of the following the dimensionless quantity is

1) Angle

2) strain

3) Relative density

4) all the above

124. Dimensional formulae are used

a) to convert one system of units into another

b) to find proportionality constants

c) to check the correctness of an equation

1) only a &b are true

2) only c is true

3) a & c are true

4) all the true

125. (A): The correctness of an equation is verified using the principle of homogeneity.

(B): All unit less quantities are dimensional less.

1) Both A & B are true

2) Both A & B are false

3) only A is true

4) only B is true

126. (A): The value of dimensionless constants or proportionality constants cannot be found by dimensional methods.

(B): The equations containing trigonometrically, exponential and logarithmic functions cannot be analysed by dimensional methods.

1) Both A & B are true

2) Both A & B are false

3) only A is true

4) only B is true

127. Which of the following is not a unit of time

a) par – sec

b) light – year

c) micron

d) sec

1) only a

2) a and b

3) a, b, & c

4) a, b, c, d

128. Which of the following is dimensionless

a) Boltzmann constant

b) Planks constant

c) Poissons ratio

d) Relative density

1)both a &b

2)both b &c

3) both c & d

4) both d & a

129. For a body in a uniformly accelerated motion, the distance of the body from a reference point at time ‘t’ is given by x=at+ bt^{2 }+ c where a, b, c are constants. The dimensions of V are the same as those of

a) x

b)at

c)bt^{2}

d) a^{2/b }

1)a

2) a &b

3) a, b & c

4) a, b, c & d

130. If e, E_{0}, h and C respectively represents electronic change, permittivity of free space, planks constant and speed of light then \frac { { e }^{ 2 } }{ { E }_{ 0 }hC } has the dimensions of

a) angle

b) relative density

c) strain

d) current

1) a,b

2)d

3) a, b, c

4) a,b,c, d

131. Photon is quantum of radiation with energy E = hv where v is frequency and h is Planck’s constant. The dimensions of h are the same as that of

a) Linear impulse

b) Angular impulse

c) Linear momentum

d) Angular momentum

1) only a

2)b and d

3) a, b, c, d

4) a and d

132. If planck’ s constant (h) and speed of light in vacuum (c) are taken as two fundamental quantities, which one of the following can, in addition, be taken to express length, mass and time in terms of the three chosen fundamental quantities?

a) Mass of electron (m_{e})

b) Universal gravitational constant (G)

c) Charage of electron (e)

d) Mass of proton(m_{p} )

1) c only

2) (a) and (c) only

3) (a) and (d) only

4) a, b and d only

133. A book with many printing errors contains four different expressions for the displacement ‘y’ of a particle executing simple harmonic motion. The wrong formula on dimensional basis (v = velocity)

i) y = A sin(2π t / T)

ii) y = A sin(Vt)

iii) y = A / Tsin(t /A)

iv) y = \frac { A }{ \sqrt { 2 } } (sin ω t + cos ω t)

1)ii only

2) ii and iii only

3) iii only

4) iii and iv only

134. List-1

a) Temperature

b) Mass

c) Length

d) Time

List – 2

e) Light Year

f) Shake

g) Fahrenheit

h) Atomi Mass unit

1)a-h, b-f, c-g, d-e

2) a – g, b – h, c – e, d – f

3) a – g, b – e, c – h, d – f

4) a – f, b – g, c – e, d- h

135. List-1

a) Second

b) Mole

c) Metre

d) Kilogram

List – 2

e) Carbon – 12

f) Platinum iridium

g) Cs – 133

h) Kr – 86

1)a-e, b-g, c-h, d-f

2)a-f,b-h,c-g, d-e

3) a – e, b – f, c – h, d – g

4) a – g, b – e, c – h, d- f

136. List-1

a) m^{-1}

b)Pa

c) JK^{-1}

d) J m^{-2}

List – 2

e) Surface tension

f) Thermal capacity

g) Rydberg constant

h) Energy density

1)a-h, b-f, c-e, d-g

2)a-g,b-h,c-e,d-f

3) a – g, b – h, c – f, d – e

4) a – f, b – e, c – g, d- h

137. List-1

a) Electron volt

b) kWH

c) Horse power

d) Fermi

List – 2

e) 746 W

f) 10^{-15} m

g) 36 x 10^{5 }J

h) 1.6x 10^{-19}J

1) a- h, b – g, c – e, d – f

2) a – h, b – f, c – g, d – e

3) a – g, b – h, c – e, d-f

4) a – h, b – g, c – f, d- e

List -1

a) Pressure

b) Latent heat

c) Velocity gradient

d) Magnetic flux

List – 2

e) ML^{2 T-2 I-1f) M0 L0 T-1g) ML-1 T-2h) M0 L2 T-2 }

1) a – h, b – f, c – g, d – e

2) a – g, b – h, c – e, d – f

3) a – g, b – h, c – f, d – e

4) a – f, b – g, c – e, d- h

139. List-1

a) Surface Tension

b) Specific heat

c) Latent heat

d) Kinematic viscosity

List – 2

e) Gas constant

f) Areal velocity

g) Spring constant

h) Gravitational potential

1) a – e,b – g, c – h, d – f

2) a – f, b – h, c – g, d – e

3) a – g, b – f, c – h, d – e

4) a – g, b – e, c – h, d – f

140. List-1

^{a) Same negative dimensions of massb) Same negative dimensions of lengthc) Same dimensions of timed) Same dimensions of current List – 2}

e) Pressure, Rydberg constant

f) Magnetic induction field, potential

g) Capacity, Universal gravitational constant

h) Energy density, Surface tension

1) a-g, b-e, c-h, d-f

2) a – g, b – h, c – e, d – f

3) a – e, b – f, c – g, d – h

4) a – f, b – e, c – h, d – g

141. Some physical constants are given in List- I and their dimensional formulae are given in List-2. Match the correct pairs in the lists

List -1

a) Planck’s constant

b) Gravitational constant

c) Bulk modulus

d) Coefficient of viscosity

List-2

e) ML, ^{-1}T^{2}

f) ML^{-1}T^{-1}

g) ML^{2}T^{-1}

h) M^{-1}L^{3}T^{-2}

1) a – h, b – g, c – f, d – e

2) a – f, b – e, c – g, d – h

3) a – g, b – f, c – e, d – h

4) a – g, b – h, c – e, d – f

142. Names of units of some physical quantities are given in List-1 and their dimensional formulae are given

in List- 2, Match correct pair in lists

List -1

a) pa s

b) NmK^{-1}

c) Jkg-‘K-1

d) Wm^{-1}K^{-1}

List – 2

e) L^{2}T^{-2}K^{-1}

f) MLT^{-3}K^{-1}

g) ML^{-1}T^{-1}

h) ML^{2}T^{–}K^{-1}

1)a-h, b-g, c-e, d-f

2) a – g, b – f, c – h, d – e

3) a. – g. h – e, c – h, d – f

4) a – g, b – h, c – e, d – f

The density of mercury in cgs system is 13.6 g cm^{–}3. Its value in SI is

136kg/m^{3}

2) 1360 kg/m^{3}

3) 13600 kg/m^{3}

4) 1.36 kg/m^{3}

A force of 40N acts on a body. If the units of mass and length are doubled and the unit of time is tripled, force in the new system becomes

90N

2) 90 new units

3) 160/9 new units

4)160/9 N

If the unit of force were 10N, that of power were 1MW and that of time were 1 millisecond then the unit would be

1) 1m

2) 100m

3)10^{3}m

4)10^{-2}m

If the unit of power is million erg/minute, the unit of force is 1000 dyne and the unit of length is 5/3 cm then the unit of time is (in second)

1) 10

2) 1

3) 1/10

4) 1/100

If the unit of length is doubled, unit of time is halved and unit of force is quadrupled, the unit of power would change by the factor

4-Jan

2)16

3)1/16

4)8

6. The volume V of a liquid crossing through a tube is related to the area of cross-section A, velocity v and times t as V ∝ A^{a}v^{b}t^{c }which of the following is correct

A is not equal to b is not equal to c

2)a = b = c

3) a ≠ b = c

4) a=b ≠ c

The critical velocity v of a body depends on the coefficient of viscosity η the density d and radius of the drop r. If K is a dimensionless constant then v is equal to

1) ( K η d)/r

K d /(ηr)

(K η)/d r

Kr/(ηr)

8. If density (D), acceleration (a) and force (F) are taken as basic quantities, then Time period has dimensions

1/6 in F

2)-1/6 in D

3)-2/3in a

4) All the above are true

The critical angular velocity w of a cylinder inside another cylinder containing a liquid at which its turbulence occurs depends on viscosity eta, density d and the distance x between the walls of the cylinders. Then w is proportional to

η/(x^{2}d)

η/ (d^{2}x)

η x^{2}/(xd)

(x d)/& eta;

10. The liquid drop of density ρ, radius r and surface tension a oscillates with time period T. Which of the following expression for T^{2} is correct.

1) ρr^{3}/&;sigma

2) ρ σ /r^{3}

3) r^{3}σ /ρ

4) None

11. The volume of a liquid (v) flowing per second through a cylindrical tube depends upon the pressure gradient (p/l) radius of the tube (r) coefficient of viscosity (η) of the liquid by dimensional method the correct formula is

1) V ∝ [(Pr^{4})/( ηl)]

2) V ∝ [(Pr)/ (ηl^{4})]

3) V ∝ [(Pl^{4})/ (ηr)]

4) none

12. The dimensions of resistivity in terms of M, L, T and Q, where Q stands for the dimensions of charge is

1) ML^{3}T^{-1}Q^{–}2

2) ML^{3}T^{-2}Q^{-1 }

3) ML^{2}T^{-1}Q^{-1}

4) MLT^{-1}Q^{-1}

13. The distance travelled by a particle in n^{th} second is S^{n} = u + \frac { a }{ 2 } (2n – 1) where u is the velocity and a is the acceleration. The equation is

1) dimensionally true

2) dimensionally false

3) numerically may be true or false

4) 1 and 3 are correct

The position of a particle at time ‘t’ is given by the equation : x(t) = \frac { V_{0} }{A } (1 – e^{At}); V_{0}= constant and A > 0. dimensions of V_{0} and A respectively are ;

M^{0}LT^{° }and T^{-1}

2) M^{0}LT^{-1} and LT^{-2 }

3) M^{0}LT^{-1} and T

4) M^{0}LT-1 and T^{-1}

If J is the angular momentum and E is the kinetic energy, then J^{2}/E has the dimensions

Moment of Inertia

2) Power

3) Angular velocity

4) Impulse

If L is the inductance, C is the capacitance and R is the resistance, then R \sqrt { \frac { C }{ L } } has the dimension

MLT^{ -2} I^{ -2}

2)ML^{ 2} T^{ 2} I

3) ML^{ -1} T^{ -2}^{ I-1 }

4)M^{ 0} L^{ 0} T^{ 0} I^{ 0}

If h is Planck’s constant and, &lamda;is the wavelength, h/&lamda; has the dimensions of

Energy

2) Momentum

3) Moment of Inertia

4) Frequency

The power of a motor is 200W. If the unit of length is halved, that of mass is doubled and that of time is Ac doubled, then the power of the motor in the new system is

3200 W

2) 3200 new units

3) 12.5 new units

4) 12.5 W

If the unit of mass is α kg, the unit of length is β metre and the unit of time is ‘ γ ‘ second, The magnitude of calorie in the new system is (1 Cal = 4.2 J)

4.2α ^{2} β^{2} γ ^{2 }new units

2) 4.2 α^{-1 }β ^{-2 }γ ^{2} new units

α^{ -1 }β^{ -2} γ ^{2} new units

4) (1/4.2) α ^{-1 }β^{ -2} γ ^{2 }new units

If the mass of the electron (9x 10^{-31}kg) is taken as unit of mass, the radius of the first Bohr orbit 0.5×10^{-10}m) as unit of length and 500 newton as the unit of force, then the unit of time in the new system would be

3×10^{-22}s

2) 15 x 10^{-12}s

3) 15 x 10^{-20}s

4) 45 x 10^{-20}s

If pressure P, velocity of light C and acceleration due to gravity g are chosen as fundamental units, then dimensional formula of mass is

PC^{3}g^{-4}

2) PC^{-4}g^{3}

3) PC^{4}g^{-3 }

4) PC^{4}g^{3}

If young’s modulus y, surface tension s and time t are the fundamental quantities then the dimensional formula of density is

1) s^{2}s^{3}t^{-2}

2) s^{3}y^{3}T^{-2 }

3) s^{-2}y^{3}T^{2 }

4) s^{-2} y^{2}T^{3}

If P represents radiation pressure, C speed of light, and Q radiation energy striking unit area per second and x,y,z are non zero integers, then P^{x }Q^{y} C^{z} is dimensionless. The values of x,y and z are respective

1,1,-1

2)1,-1,1

3)-1,1,1

4)1,1,1

If the time period (T) of vibration and liquid drop depends on surface tension (S), radius (r) of the drop and density (ρ) of the liquid, then the expression of T is

T=K\frac { \sqrt { { \& rho; }{ r }^{ 3 } } }{ { S }^{ 2 } }

T=K\frac { \sqrt { { \& rho; }^{ 1/2 }{ r }^{ 3 } } }{ { S } }

T=K\frac { \sqrt { { \& rho; }{ r }^{ 3 } } }{ { S }^{ 1/2 } }

T=K\frac { \sqrt { { \& rho; }^{1/ 2 }{ r }^{ 3 } } }{ { S } }

Suppose, the torque acting on a body is given by T=KL+xI/(ω) . Where L = angular- momentum, I= moment of inertia, omega= angular speed. The dimensional formula for Kx is same as that for

1)time^{2}

2) time^{4}

3) time^{-2}

4) time^{-4}

The number of particles crossing unit area perpendicular to x-axis in unit time is given by n=-[-D(n_{2}-n_{1})]/[x_{2}-x_{1}]where n_{1} and n_{2} are number of particles per unit volume for the value of x meant to x_{1}and x_{2}. The dimensions of D are

1) M^{0}L T^{3}

2) M^{0}L^{2}T^{-2}

3) M^{0}L T^{-2}

4) M^{0}L^{2} T^{-1}

10. Turpentine oil is flowing through a capillary tube of length 1 and radius r. The pressure difference between the two ends of the tube is P. The viscosity of oil is given by : η=[P(r^{2}-x^{2})]/[4vl]fd. Here v is velocity of oil at a distance x from the axis of the tube. From this relation, the dimensional formula of η is

( ML^{-1}T^{-1})

2)[MLT^{-1}]

3) [ML^{2}T^{-2}]

4) [M^{0}L^{0}T^{0}]

11. Dimensional formula of the product of the two physical quantities P and Q is ML^{2}T^{-2}, the dimension formula of (P/Q) is MT^{ -2}. P and Q respectively are

1) Force, velocity

2) Momentum, displacement

3) Force, displacement

4) Work, velocity

12. The potential energy of a particle varies with distance x from a fixed origin as V = \frac { A\sqrt { x } }{ x+B } where A and B are constants. The dimensions of AB are

1) M^{1}L^{5/2}T^{=2}

2) M^{1}L^{2}T^{=2 }

3) M^{3/2}L^{5/2} T^{-2}

4) M^{1}L^{7/2}T^{-2}

13. If h is the Planck’s constant, m = mass of die electron, e – charge of the electron and ε_{0 }= permittivity of vacuum, then [(h^{2}ε_{0})/(me^{2})] has the unit

1)newton

2) joule

3} watt

4) metre

ii the displacement y of a particle is y = A sin(pt + qx), then dimensional formula of ‘ Apq ‘ is

L

2) LT^{-1 }

3)T^{-1 }

4) L^{-1} T^{-1}

A circular railway track of radius r is banked at angle θ so that a train moving with speed u can safely go round the track. A student writes : tan θ = rg/v^{2} Why this relation is not correct ?

Equality of dimensions does not guarantee correctness of the relation.

Dimensionally correct relation may not be numerically correct.

The relation is dimensionally incorrect.

i)&(ii)

2)(ii)&(iii)

3)(iii)&(i)

4) (i), (ii) & (iii)

The parameter \frac { m{ Q }^{ 4 } }{ { { \varepsilon }_{ 0 } }^{ 2 }{ h }^{ 2 } } has the dimensions of (m = mass, Q = charge, epesolonat _{0} Permittivity and h = Planck’s constant)

Wavelength

2) Power

3) Angular momentum

4) Energy

The dimensional formula of( 1/2) ε_{0} E^{2} is(ε_{0} is permittivity of free space and E is electric field)

ML^{2}T^{-2}

2)MLT^{-2}

3) ML^{-1}T^{-2}

4) ML ^{-2}T^{-1}

!f M is the magnetic moment, B is the magnetic induction and T is the time, then MBT^{2 }has the dimensions

Intensity of magnetization

2) Intensity of magnetic field

Moment of Inertia

4) Magnetic permeability

A quantity X is given by { \varepsilon }_{ 0 }L\frac { \triangle V }{ \triangle t } where ε _{0} is the permittivity of free space, L. is a length delta V is a potential difference and delta t is a time interval. The dimensional formula for X is the same as that of

resistance

2) charge

3) voltage

4) current

Pressure depends on distance as, P=\frac { \alpha }{ \beta } exp(-\frac { \alpha z }{ k\theta } ) where α, β are constants, z is distance, ‘k’ is Boltzmann’s constant and ‘ θ ‘ is temperature. The dimension of β are

M^{0}L^{0}T ^{0}

2) M^{-1}L^{-1}T^{-1}

3) M^{0}L^{2}T^{0}

4) M^{-1}L^{1}T^{2
In the equation \frac { 1 }{ P\beta } =\frac { y }{ { k }_{ \Beta }T } when P is the pressure, y is the distance, kb is Boltzmann constant and T is the temperature, dimensions of beta are }

1) M^{-11}T^{2}

2) M^{0}L^{2}T^{0}

M^{1}L^{-1}T^{-2}

M^{0}L^{0}T^{0}

Assertion (A) Energy is a derived quantity

Reason (R) Energy is a scalar

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) Though Fermi is a unit of distance, it is not a fundamental unit

Reason (R) All practical units need not be fundamental units

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) In mechanics, we treat length, mass and time as the three basic or fundamental quantities.

Reason (R) Length, mass and time cannot be obtained from one another.

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) Light year is a unit of time.

Reason (R) Light year is the distance travelled by light in vacuum in one year.

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) The magnitude of a physical quantity does not change when the system of units is changed from S.I system to C.G.S system.

Reason (R)The magnitude of a physical quantity is independent of system of units

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A)When we change the unit of measurement of a quantity, its numerical value changes

Reason (R)Smaller the unit of measurement smaller is its numerical value.

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A)Electric current is a scalar

Reason (R) All fundamental physical quantities are scalars.

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A)If u_{1} and u_{2 }are units and n_{1} n_{2} are their numerical values in two different systems then n_{1} > n_{2} & u_{1}< u_{2}.

Reason (R) The numerical value of physical quantity is inversely proportional to unit

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) The equation y = x + t cannot be true where x, y are distances and t is time

Reason (R) Quantities with different dimensions cannot be added

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) Plane angle is a dimensionless quantity

Reason (R)All unit less quantities are dimensionless

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) Dimensions of constant of proportio-nalities can be derived from dimensional method

Reason (R)Numerical value of constant of proportion-ality can be found from experiments only.

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) Angular momentum and Plank’s constant are dimensionally similar but they are not identical physical quantities

Reason (R)Dimensionally similar quantities need not be identical

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) A dimensionally correct equation may not be a correct equation of usage

Reason (R) Every expression which is dimensionally correct need not be numerically correct

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) The Dimensional formula of a physical quantity is same in any system of units.

Reason (R)Dimensional formula is independent of system of units.

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) Solid angle is a dimensionless quantity and it is a supplementary quantity

Reason (R) All supplementary quantities are dimensionless

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) The dimensional formula for relative velocity is same as that of the change in velocity

Reason (R) Relative velocity of P w.r.t. Q is the ratio of velocity of P and that of Q

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) Energy cannot be divided by volume.

Reason (R) Dimensions of energy and volume are different.

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true

Assertion (A) The time period of a pendulum is given by the formula, T=2\pi \sqrt { \frac { g }{ l } } .

Reason (R)According to the principle of homogeneity of dimensions, only that formula is correct in which the dimensions of L.H.S. equal to dimensions of R.H.S

1) Both (A) and (R) are true and (R) is the correct explanation of (A)

2) Both (A) and (R) are true and (R) is not the correct explanation of (A)

3) (A) is true but (R) is false

4) (A) is false but (R) is true