# test latex

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

1)105
2) 10-5
3) 10-6
4) 10-7
The dimensional formula of a pseudo force is

1) M0L0T-1
2) M0L0T0
3) M 0L T0
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)107
2)10-7
3) 105
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
19. SI unit of Stefan’s constant is

1)w m-2 K-4
2) J m-2K-4
3)W m-1 K-1
4) W m-2 K-2
20. SI unit of Thermal resistance is

Wk-1
2)W-1k
3)W-1k-1
4) Wm-1k-1
21. If the units of length, mass and time are doubled, the unit of force will be

1) doubled
2) halved
4) unchanged
22. If U1 and U2 are the units of a physical quantity and n1 and n2 are its numerical values, then

1) n1/n2=U1/U2
2)n1/n2= \sqrt { \frac { U1 }{ U2 } }
3) (n1/n2)2= U1/U2
4)n1/n2=U2/U1
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
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.

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-1T
2) ML-1T-1
3) MLT-1
4) M-1L-1T
Dimensional formula of Intensity of Magnetization is

1)IL
2)IL-2
3)IL-1
4) I-1L
ML -1T-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) ML2 T-3 I2
2) M-1 L-3 T4 I2
3) M-1L-2T4I2
4) M-1L-2T-3I2
The dimensional formula of the physical quantity whose S.I. unit is Hnv1 is

1) ML2 T-2 I2
2) M L T-2I-2
3) M2 L2 T-2I-2
4) ML T2I2
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
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
(x2/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)M0L2T
2)M0L2T-1
3) M0 L3T-1
4) M0 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-1T
3) ML-1T-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-1A-1
2) MT-2A-1
3) MTA-2
4) MT-2A
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/m2
2)kgm2
3) N/m2
4) Nm2
Dimensional formula of capacitance is

1) M-1L-2T-4I2
2) M-1L-2T4I2
3) ML2T-4I2
4) ML-2T4I-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 103 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/m2
2) Am2
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 1010
3) 3.6 x 1013
4) 3.6 x 1011
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-1L-2T3K1
2) M0L0T-2
3) MLT4
4) MLT-1
86. The dimensional formula of velocity gradient is

1) M0L0T-1
2) MLT-1
3) ML0T-1
4) M0LT-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) M0L-1T-1
2) M0L2T-1
3) ML2T-1
4) ML-1T-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) ML2T-2
3) M0L2T-2
4) MLT-1
91. ML-1T-2 represents

1) Stress
2) Young’s modulus
3) Pressure
4) All the above
92. Dimensional formula for angular momentum is

1) ML2T-1
2) ML3T-1
3) MLT-1
4) ML3T-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 ML2T-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) M2LT-2
2) ML2T-2
3) M-1L2T-2
4) MLT-2
98. The dimensional formula for angular velocity is

1) M-1LT-2
2)M0L-1T0
3) M-1L-1T0
4) M0L0T-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 (μ0 ε0) -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 ∝ pa sb rc, 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
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-2T-2I-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-1Q-1
118. The dimensional formula of 1/2 ε0 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+ bt2 + c where a, b, c are constants. The dimensions of V are the same as those of
a) x
b)at
c)bt2
d) a2/b

1)a
2) a &b
3) a, b & c
4) a, b, c & d
130. If e, E0, 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 (me)
b) Universal gravitational constant (G)
c) Charage of electron (e)
d) Mass of proton(mp )

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 105 J
h) 1.6x 10-19J

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
d) Magnetic flux
List – 2

e) ML2 T-2 I-1
f) M0 L0 T-1
g) ML-1 T-2
h) 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 mass
b) Same negative dimensions of length
c) Same dimensions of time
d) 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, -1T2
f) ML-1T-1
g) ML2T-1
h) M-1L3T-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-1K-1
List – 2

e) L2T-2K-1
f) MLT-3K-1
g) ML-1T-1
h) ML2TK-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 cm3. Its value in SI is

136kg/m3
2) 1360 kg/m3
3) 13600 kg/m3
4) 1.36 kg/m3
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)103m
4)10-2m
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 ∝ Aavbtc 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/(x2d)
η/ (d2x)
η x2/(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 T2 is correct.

1) ρr3/&;sigma
2) ρ σ /r3
3) r3σ /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 ∝ [(Pr4)/( ηl)]
2) V ∝ [(Pr)/ (ηl4)]
3) V ∝ [(Pl4)/ (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) ML3T-1Q2
2) ML3T-2Q-1
3) ML2T-1Q-1
4) MLT-1Q-1
13. The distance travelled by a particle in nth second is Sn = 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 { V0 }{A } (1 – eAt); V0= constant and A > 0. dimensions of V0 and A respectively are ;

M0LT° and T-1
2) M0LT-1 and LT-2
3) M0LT-1 and T
4) M0LT-1 and T-1
If J is the angular momentum and E is the kinetic energy, then J2/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 β2 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 10-31kg) is taken as unit of mass, the radius of the first Bohr orbit 0.5×10-10m) as unit of length and 500 newton as the unit of force, then the unit of time in the new system would be

3×10-22s
2) 15 x 10-12s
3) 15 x 10-20s
4) 45 x 10-20s
If pressure P, velocity of light C and acceleration due to gravity g are chosen as fundamental units, then dimensional formula of mass is

PC3g-4
2) PC-4g3
3) PC4g-3
4) PC4g3
If young’s modulus y, surface tension s and time t are the fundamental quantities then the dimensional formula of density is

1) s2s3t-2
2) s3y3T-2
3) s-2y3T2
4) s-2 y2T3
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 Px Qy Cz 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)time2
2) time4
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(n2-n1)]/[x2-x1]where n1 and n2 are number of particles per unit volume for the value of x meant to x1and x2. The dimensions of D are

1) M0L T3
2) M0L2T-2
3) M0L T-2
4) M0L2 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(r2-x2)]/[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-1T-1)
2)[MLT-1]
3) [ML2T-2]
4) [M0L0T0]
11. Dimensional formula of the product of the two physical quantities P and Q is ML2T-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) M1L5/2T=2
2) M1L2T=2
3) M3/2L5/2 T-2
4) M1L7/2T-2
13. If h is the Planck’s constant, m = mass of die electron, e – charge of the electron and ε0 = permittivity of vacuum, then [(h2ε0)/(me2)] 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/v2 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) ε0 E2 is(ε0 is permittivity of free space and E is electric field)

ML2T-2
2)MLT-2
3) ML-1T-2
4) ML -2T-1
!f M is the magnetic moment, B is the magnetic induction and T is the time, then MBT2 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

M0L0T 0
2) M-1L-1T-1
3) M0L2T0
4) M-1L1T2
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-11T2
2) M0L2T0
M1L-1T-2
M0L0T0
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 u1 and u2 are units and n1 n2 are their numerical values in two different systems then n1 > n2 & u1< u2.
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