1Units, Dimensions and Errors

📚
PHYSICAL QUANTITIES AND UNITS
▢ Physical quantity: Measurable property = numerical value × unit
▢ Unit: Defined standard for comparison
▢ Requirements of standard unit:
  • •
    Well-defined
  • •
    Invariable
  • •
    Reproducible
  • •
    Accessible
  • •
    Internationally accepted
▢ Systems:
❖ CGS: centimetre–gram–second
❖ MKS: metre–kilogram–second
❖ FPS: foot–pound–second
❖ SI: 7 base units + coherent derived units
▢ Unit notation rules:
  • •
    Unit symbols: upright; no plural; no full stop
  • •
    Space between value and unit: \(25\,kg\), \(37\,^\circ C\)
  • •
    Named-person symbols uppercase: N, J, Pa, W; names lowercase: newton, joule
  • •
    Prefix joined directly: mm, μm, kJ
  • •
    Only one prefix per unit; \(1\,\mu m=10^{-6}\,m\)
📚
FUNDAMENTAL UNITS
Image 1
Fig.Fundamental quantities

Table 1: SI base quantities and units

S.N.
Base quantity
Quantity symbol
SI unit
Unit symbol
1.
Length
L
metre
m
2.
Mass
M
kilogram
kg
3.
Time
T
second
s
4.
Electric current
I
ampere
A
5.
Thermodynamic temperature
\(\Theta\)
kelvin
K
6.
Luminous intensity
\(J\)
candela
cd
7.
Amount of substance
\(N\)
mole
mol
📚
SUPPLEMENTARY UNITS

Table 1: Angle units

S.N.
Quantity
Quantity symbol
SI unit
Unit symbol
1.
Plane angle
\(\theta\)
radian
rad
2.
Solid angle
\(\Omega\)
steradian
sr
Radian and steradian: dimensionless derived SI units; traditionally called supplementary units.
📚
DERIVED UNITS

Table 1: Common derived quantities

S.N.
Physical quantity
Defining relation
Dimensional formula
SI unit
1.
Area
Length × Length
[L²]
m²
2.
Volume
Length³
[L³]
m³
3.
Density
Mass / Volume
[ML⁻³]
kg m⁻³
4.
Velocity
Displacement / Time
[LT⁻¹]
m s⁻¹
5.
Acceleration
Velocity / Time
[LT⁻²]
m s⁻²
6.
Momentum
Mass × Velocity
[MLT⁻¹]
kg m s⁻¹
7.
Force
Mass × Acceleration
[MLT⁻²]
N
8.
Impulse
Force × Time
[MLT⁻¹]
N s
9.
Work / Energy
Force × Displacement
[ML²T⁻²]
J
10.
Power
Work / Time
[ML²T⁻³]
W
11.
Pressure
Force / Area
[ML⁻¹T⁻²]
Pa
12.
Stress
Force / Area
[ML⁻¹T⁻²]
Pa
13.
Strain
ΔLength / Original Length
Dimensionless
1
14.
Young’s Modulus
Stress / Strain
[ML⁻¹T⁻²]
Pa
15.
Surface Tension
Force / Length
[MT⁻²]
N m⁻¹
16.
Viscosity (η)
Stress / Velocity Gradient
[ML⁻¹T⁻¹]
Pa s
17.
Angular Displacement
θ (arc length / radius)
Dimensionless
rad
18.
Angular Velocity
θ / Time
[T⁻¹]
rad s⁻¹
19.
Angular Acceleration
Angular velocity / Time
[T⁻²]
rad s⁻²
20.
Moment of Inertia
Mass × Radius²
[ML²]
kg m²
21.
Torque
Force × Perpendicular distance
[ML²T⁻²]
N m
22.
Angular Momentum
Moment of inertia × Angular velocity
[ML²T⁻¹]
kg m² s⁻¹
23.
Frequency
1 / Time
[T⁻¹]
Hz
24.
Wavelength
Wave speed / Frequency
[L]
m
25.
Wave number
1 / Wavelength
[L⁻¹]
m⁻¹
26.
Wave speed
Wavelength × Frequency
[LT⁻¹]
m s⁻¹
27.
Energy density
Energy / Volume
[ML⁻¹T⁻²]
J m⁻³
28.
Heat
Work (Joule equivalent)
[ML²T⁻²]
J
29.
Temperature gradient
Δθ / Length
\([L^{-1}\Theta]\)
K m⁻¹
30.
Thermal conductivity
\(k=\dfrac{QL}{A\,\Delta T\,t}\)
\([MLT^{-3}\Theta^{-1}]\)
W m⁻¹ K⁻¹
31.
Gravitational potential
Work / Mass
[L²T⁻²]
J kg⁻¹
32.
Gravitational field intensity
Force / Mass
[LT⁻²]
N kg⁻¹
33.
Gravitational constant (G)
F r² / (m₁m₂)
[M⁻¹L³T⁻²]
N m² kg⁻²
34.
Electric charge
Current × Time
[IT]
C
35.
Electric field
Force / Charge
[MLT⁻³I⁻¹]
N C⁻¹ = V m⁻¹
36.
Electric potential
Work / Charge
[ML²T⁻³I⁻¹]
V
37.
Potential gradient
Electric potential / Length
[MLT⁻³I⁻¹]
V m⁻¹
38.
Capacitance
Charge / Potential
[M⁻¹L⁻²T⁴I²]
F
39.
Resistance
Potential difference / Current
[ML²T⁻³I⁻²]
Ω
40.
Resistivity
Resistance × Area / Length
[ML³T⁻³I⁻²]
Ω m
41.
Conductivity
1 / Resistivity
[M⁻¹L⁻³T³I²]
S m⁻¹
42.
Electric power
Current × Voltage
[ML²T⁻³]
W
43.
Magnetic flux
Magnetic field × Area
\([ML^2T^{-2}I^{-1}]\)
Wb
44.
Magnetic flux density (B)
Force / (Charge × Velocity)
[MT⁻²I⁻¹]
T
45.
Permeability
B × Length / Current
[MLT⁻²I⁻²]
H m⁻¹ = N A⁻²
46.
Inductance
Magnetic flux / Current
[ML²T⁻²I⁻²]
H
47.
Self-inductance
Induced emf × Time / Current
[ML²T⁻²I⁻²]
H
48.
Mutual inductance
Flux linkage / Current in other coil
[ML²T⁻²I⁻²]
H
49.
Emf
Work / Charge
[ML²T⁻³I⁻¹]
V
50.
Luminous flux
Luminous intensity × Solid angle
\([J]\)
lm
51.
Illuminance
Luminous flux / Area
\([JL^{-2}]\)
lx
52.
Radiant flux
Energy / Time
[ML²T⁻³]
W
53.
Radiant intensity
Power / Solid angle
\([ML^2T^{-3}]\)
W sr⁻¹
54.
Specific heat capacity
Heat / (Mass × ΔT)
[L²T⁻²θ⁻¹]
J kg⁻¹ K⁻¹
55.
Entropy
Heat / Temperature
[ML²T⁻²θ⁻¹]
J K⁻¹
56.
Coefficient of Thermal expansion
ΔL / (L ΔT)
[θ⁻¹]
K⁻¹
57.
Planck’s constant
Energy / Frequency
[ML²T⁻¹]
J s
58.
Stefan-Boltzmann constant
Power / (Area × T⁴)
[MT⁻³θ⁻⁴]
W m⁻² K⁻⁴
59.
Universal gas constant
PV / nT
\([ML^2T^{-2}\Theta^{-1}N^{-1}]\)
J mol⁻¹ K⁻¹
60.
Boltzmann constant
R / NA
\([ML^2T^{-2}\Theta^{-1}]\)
J K⁻¹
61.
Spring constant
\(k=F/x\)
\([MT^{-2}]\)
N m⁻¹
62.
Modulus of rigidity
Shear stress / shear strain
\([ML^{-1}T^{-2}]\)
Pa
63.
Permittivity
\(\varepsilon=C\,d/A\)
\([M^{-1}L^{-3}T^4I^2]\)
F m⁻¹
64.
Specific latent heat
\(L=Q/m\)
\([L^2T^{-2}]\)
J kg⁻¹
65.
Coefficient of friction
\(\mu=F/N\)
Dimensionless
1
66.
Refractive index
\(n=c/v\)
Dimensionless
1
📚
SI PREFIXES

Table 1: Positive and negative SI prefixes

Positive power
Prefix
Symbol
Negative power
Prefix
Symbol
\(10^{24}\)
yotta
Y
\(10^{-24}\)
yocto
y
\(10^{21}\)
zetta
Z
\(10^{-21}\)
zepto
z
\(10^{18}\)
exa
E
\(10^{-18}\)
atto
a
\(10^{15}\)
peta
P
\(10^{-15}\)
femto
f
\(10^{12}\)
tera
T
\(10^{-12}\)
pico
p
\(10^{9}\)
giga
G
\(10^{-9}\)
nano
n
\(10^{6}\)
mega
M
\(10^{-6}\)
micro
μ
\(10^{3}\)
kilo
k
\(10^{-3}\)
milli
m
\(10^{2}\)
hecto
h
\(10^{-2}\)
centi
c
\(10^{1}\)
deca
da
\(10^{-1}\)
deci
d
\(10^0=1\): no prefix
📚
DIMENSIONS
▢ Dimensional formula: \([Q]=[M^aL^bT^cI^d\Theta^eN^fJ^g]\)
▢ Dimensional equation: Physical quantity = dimensional formula; e.g. \([F]=[MLT^{-2}]\)
▢ Principle of homogeneity: Every additive term in a valid physical equation has identical dimensions
▢ Applications:
  • •
    Checking dimensional consistency
  • •
    Deriving relation up to dimensionless constant
  • •
    Converting numerical value between unit systems
  • •
    Finding dimensions/units of constants
▢ Unit conversion:
❖ General: \(n_1[M_1^aL_1^bT_1^c\cdots]=n_2[M_2^aL_2^bT_2^c\cdots]\)
❖ Numerical value: \(n_2=n_1\left(\dfrac{M_1}{M_2}\right)^a\left(\dfrac{L_1}{L_2}\right)^b\left(\dfrac{T_1}{T_2}\right)^c\cdots\)
❖ Example: \(1\,N=10^5\,dyne\)
▢ Dimensionless quantities:
❖ Without unit:
  • •
    Strain
  • •
    Refractive index
  • •
    Relative density
  • •
    Coefficient of friction
  • •
    Poisson ratio
❖ With named unit:
  • •
    Plane angle → rad
  • •
    Solid angle → sr
▢ Same dimensions:
  • •
    Work = energy = torque → \([ML^2T^{-2}]\)
  • •
    Impulse = linear momentum → \([MLT^{-1}]\)
  • •
    Pressure = stress = elastic modulus = energy density → \([ML^{-1}T^{-2}]\)
  • •
    Frequency = angular velocity = velocity gradient → \([T^{-1}]\)
  • •
    Planck constant = angular momentum → \([ML^2T^{-1}]\)
▢ Limitations:
  • •
    Cannot determine dimensionless numerical constants: \(2,\pi,e\)
  • •
    Cannot distinguish different quantities with same dimensions
  • •
    Cannot determine scalar/vector nature
  • •
    Cannot establish additive/trigonometric/exponential form
  • •
    Dimensionally correct equation may be physically incorrect
📚
SCIENTIFIC NOTATION AND SIGNIFICANT FIGURES
▢ Scientific notation: \(N=a\times10^n\), \(1\le |a|<10\)
▢ Order of magnitude: Nearest integral power of 10
▢ Significant figures:
❖ Definition: All certain digits + first uncertain digit
❖ Counting rules:
  1. All non-zero digits significant
  2. Zeros between non-zero digits significant
  3. Leading zeros not significant
  4. Trailing zeros significant only when decimal point/precision is explicit
  5. Exact counted numbers and defined conversions → infinite significant figures
  6. Scientific notation: only coefficient digits count
❖ Examples:
  • •
    \(0.00450\) → 3 s.f.
  • •
    \(2.0300\) → 5 s.f.
  • •
    \(1500\) → ambiguous; \(1.500\times10^3\) → 4 s.f.
❖ Rounding:
  • •
    Discarded first digit <5 → unchanged
  • •
    >5 → preceding digit +1
  • •
    Exactly 5 followed by non-zero → +1
  • •
    Exactly 5 followed only by zeros → round to even
❖ Operations:
◉ Multiplication/division: Result → least significant figures among inputs
◉ Addition/subtraction: Result → least decimal places among inputs
◉ Logarithm: Mantissa decimal places = significant figures of argument
◉ Antilogarithm: Result significant figures = mantissa decimal places
📚
MEASUREMENT AND ERRORS
▢ Accuracy: Closeness to true/accepted value
▢ Precision: Repeatability; closeness among repeated readings
▢ Least count: Smallest directly measurable increment
▢ Types of error:
❖ Systematic:
  • •
    Instrumental/zero error
  • •
    Environmental error
  • •
    Observational/personal error
  • •
    Theoretical error
❖ Random: Unpredictable fluctuations; reduced by repeated measurements
❖ Gross: Carelessness, wrong recording/calculation
❖ Backlash: Lost motion due to worn screw threads; approach final reading in one rotational direction
▢ Repeated measurements:
❖ Mean: \(\bar{x}=\dfrac{x_1+x_2+\cdots+x_n}{n}\)
❖ Individual absolute error: \(\Delta x_i=|x_i-\bar{x}|\)
❖ Mean absolute error: \(\Delta\bar{x}=\dfrac{\sum|x_i-\bar{x}|}{n}\)
❖ Relative/fractional error: \(\dfrac{\Delta\bar{x}}{\bar{x}}\)
❖ Percentage error: \(\dfrac{\Delta\bar{x}}{\bar{x}}\times100\%\)
❖ Reported result: \(x=\bar{x}\pm\Delta\bar{x}\)
▢ Error propagation:
❖ Addition: \(z=x+y\Rightarrow\Delta z=\Delta x+\Delta y\)
❖ Subtraction: \(z=x-y\Rightarrow\Delta z=\Delta x+\Delta y\)
❖ Multiplication: \(z=xy\Rightarrow\dfrac{\Delta z}{|z|}=\dfrac{\Delta x}{|x|}+\dfrac{\Delta y}{|y|}\)
❖ Division: \(z=x/y\Rightarrow\dfrac{\Delta z}{|z|}=\dfrac{\Delta x}{|x|}+\dfrac{\Delta y}{|y|}\)
❖ Power: \(z=x^n\Rightarrow\dfrac{\Delta z}{|z|}=|n|\dfrac{\Delta x}{|x|}\)
❖ General product: \(Q=kx^ay^bw^c\Rightarrow\dfrac{\Delta Q}{|Q|}=|a|\dfrac{\Delta x}{|x|}+|b|\dfrac{\Delta y}{|y|}+|c|\dfrac{\Delta w}{|w|}\)
❖ Derivative formula: \(Q=f(x,y,\ldots)\Rightarrow\Delta Q_{max}\approx\left|\dfrac{\partial Q}{\partial x}\right|\Delta x+\left|\dfrac{\partial Q}{\partial y}\right|\Delta y+\cdots\)
▢ Worked examples:
❖ Addition and subtraction:
◉ Given: \(A=(10.0\pm0.2)\,cm,\ B=(5.0\pm0.1)\,cm\)
◉ Sum: \(A+B=(15.0\pm0.3)\,cm\)
◉ Difference: \(A-B=(5.0\pm0.3)\,cm\)
❖ Multiplication:
◉ Given: \(l=(5.0\pm0.1)\,cm,\ b=(2.0\pm0.1)\,cm\)
◉ Calculation: \(A=lb=10.0\,cm^2;\ \Delta A/A=0.1/5.0+0.1/2.0=0.07\)
◉ Result: \(A=(10.0\pm0.7)\,cm^2\); percentage error \(=7\%\)
❖ Division:
◉ Given: \(s=(100\pm1)\,m,\ t=(20.0\pm0.2)\,s\)
◉ Calculation: \(v=s/t=5.00\,m\,s^{-1};\ \Delta v/v=1/100+0.2/20=0.02\)
◉ Result: \(v=(5.00\pm0.10)\,m\,s^{-1}\); percentage error \(=2\%\)
❖ Power:
◉ Given: \(r=(2.00\pm0.02)\,cm;\ V=\dfrac43\pi r^3\)
◉ Calculation: \(\Delta V/V=3\Delta r/r=3\%\)
◉ Result: \(V\approx(33.5\pm1.0)\,cm^3\)
❖ Density of cube:
◉ Relation: \(\rho=m/a^3\)
◉ Given: Mass error \(=4\%\); side error \(=3\%\)
◉ Maximum error: \(\%\Delta\rho=4+3(3)=13\%\)
▢ Important:
  • •
    For both + and −, absolute errors add
  • •
    For × and ÷, fractional/percentage errors add
  • •
    Negative exponent also contributes positively to maximum error
  • •
    Subtraction of nearly equal values may produce very large relative error
  • •
    Uncertainty normally rounded to 1 significant figure; retain 2 if first digit is 1 or 2
📚
PERCENTAGE CHANGE
▢ Exact finite change:
❖ Absolute change: \(\Delta y=y_{new}-y_{old}\)
❖ Percentage change: \(\%\Delta y=\dfrac{y_{new}-y_{old}}{y_{old}}\times100\%\)
❖ Sign: Positive → increase; negative → decrease
▢ Derivative approximation:
❖ Single variable: \(y=f(x)\Rightarrow\dfrac{\Delta y}{y}\approx\dfrac{f'(x)}{f(x)}\Delta x\)
❖ Percentage form: \(\%\Delta y\approx\dfrac{f'(x)}{f(x)}\Delta x\times100\%\)
❖ Several variables: \(\Delta y\approx\dfrac{\partial y}{\partial x}\Delta x+\dfrac{\partial y}{\partial z}\Delta z+\cdots\)
❖ Power law: \(y=kx^n\Rightarrow\%\Delta y\approx n(\%\Delta x)\)
❖ Product law: \(y=kx^az^b\Rightarrow\%\Delta y\approx a(\%\Delta x)+b(\%\Delta z)\)
▢ Exact power-law formula:
❖ Increase by \(p\%\): \(\%\Delta y=\left[\left(1+\dfrac{p}{100}\right)^n-1\right]100\%\)
❖ Decrease by \(p\%\): \(\%\Delta y=\left[\left(1-\dfrac{p}{100}\right)^n-1\right]100\%\)
▢ Examples:
❖ Electric power:
◉ Relation: \(P=I^2R\); \(R\) constant; \(I\) decreases by \(1\%\)
◉ Derivative: \(\%\Delta P\approx2(-1\%)=-2\%\)
◉ Exact: \([(0.99)^2-1]100\%=-1.99\%\)
❖ Gravity at Earth surface:
◉ Relation: \(g=GM/R^2\); \(M\) constant; \(R\) decreases by \(1\%\)
◉ Derivative: \(\%\Delta g\approx-2(-1\%)=+2\%\)
◉ Exact: \(\left[1/(0.99)^2-1\right]100\%\approx+2.03\%\)
❖ Area of circle:
◉ Relation: \(A=\pi r^2\); \(r\) increases by \(5\%\)
◉ Derivative: \(\%\Delta A\approx10\%\)
◉ Exact: \([(1.05)^2-1]100\%=10.25\%\)
▢ Use rule: Derivative formula → small percentage change; exact formula → finite/large change
📚
MEASURING INSTRUMENTS
▢ Zero correction: Zero correction \(=-\) zero error
▢ Vernier calipers:
❖ Least count: \(LC=1\,MSD-1\,VSD=\dfrac{1\,MSD}{N}\) for direct vernier
❖ Reading: \(MSR+(VSR\times LC)+\text{zero correction}\)
▢ Screw gauge:
❖ Pitch: Distance advanced in one full rotation
❖ Least count: \(LC=\dfrac{\text{pitch}}{\text{circular-scale divisions}}\)
❖ Reading: \(PSR+(CSR\times LC)+\text{zero correction}\)
❖ Backlash prevention: Rotate in same direction while taking final reading
▢ Combination of measured lengths: If each length has uncertainty \(\Delta L\), then \(L_1+L_2\) has maximum uncertainty \(2\Delta L\)
📚
COMMON CONVERSIONS

Table 1: High-yield units and conversions

Quantity/unit
Equivalent
Length
\(1\,\mathring{A}=10^{-10}\,m\); \(1\,\mu m=10^{-6}\,m\); \(1\,fm=10^{-15}\,m\)
Astronomical unit
\(1\,AU\approx1.496\times10^{11}\,m\)
Light-year
\(1\,ly\approx9.46\times10^{15}\,m\)
Parsec
\(1\,pc\approx3.086\times10^{16}\,m\approx3.26\,ly\)
Pressure
\(1\,atm=1.01325\times10^5\,Pa=760\,torr\); \(1\,torr\approx1\,mmHg\)
Energy
\(1\,eV=1.602\times10^{-19}\,J\); \(1\,W\,s=1\,J\)
Force
\(1\,N=10^5\,dyne\)
Viscosity
\(1\,Pa\,s=10\,poise\)
Magnetic field
\(1\,T=1\,Wb\,m^{-2}=1\,V\,s\,m^{-2}\)
Q1.
An A4-sized paper is measured using a meter scale. Which represents the most precise measurement?
📅CEE MBBS 2025
Q2.
Which pair has identical dimensions?
📅CEE MBBS 2025
Q3.
Student measures g as 6.65, 6.66 and 6.67 m/s². His measurements are
📅CEE MBBS 2025
Q4.
Which of the following has same dimension as stress?
📅CEE Nursing 2024
Q5.
The dimensional formula \([ML^{-1}T^{-1}]\) is of:
📅CEE MBBS 2024B
Q6.
The increasing order of unit of energy among joule, eV, calorie and erg is:
📅CEE MBBS 2024a
Q7.
External and internal diameters of a hollow cylinder are measured to be \(4.23\pm0.01\,\text{cm}\) and \(3.89\pm0.01\,\text{cm}\), respectively. The thickness of the cylinder is:
📅CEE MBBS 2023
Q8.
Dimensional formula of angular momentum is:
📅CEE MBBS 2023
Q9.
One electron volt is equal to:
📅CEE MBBS 2023
Q10.
Dimensional formula of magnetic flux is:
📅CEE MBBS 2022
Q11.
Velocity gradient is dimensionally represented as:
📅CEE BDS 2024
Q12.
Dimension formula of permeability \((\mu_0)\) is:
📅CEE BDS 2023
Q13.
Dimension of coefficient of viscosity:
📅CEE BDS 2021
Q14.
Relation between Dyne and Newton is:
📅CEE BDS 2021
Q15.
Which one of the following pairs of physical quantities has the same dimension?
📅CEE BDS 2021
Q16.
Question 171 is not visible in the uploaded source image.
📅CEE BDS 2021
Q17.
1 torrr is
📅BP 2014
Q18.
What is the dimension of capacitance?
📅BP 2013
Q19.
Dimension of which are same
📅BP 2013
Q20.
Dimension of universal gas constant is:
📅
Q21.
The least count is \(0.01 mm\). Two wires of length L1 and L2 are measured and they are connected forming a single wire. Then the measurements is:
📅BP 2012
Q22.
The dimension of Boltzmann's constant is:
📅BP 2011
Q23.
The dimensional formula for coefficient of viscosity is
📅
Q24.
In a micrometer gauge the reading is done by rotating terminal screw on account of worn out threads on circular scale in sam esense to prevent:
📅
Q25.
If force, length and time are taken a fundamental unit then the dimension of mass will be:
📅MOE 2014
Q26.
Inductance divided by resistance will have the unit:
📅MOE 2014
Q27.
Planck's constant has the dimension of:
📅MOE 2013, 2012
Q28.
Dimension of torque is::
📅MOE 2012
Q29.
Dimension of moment of inertia of a body::
📅MOE 2011
Q30.
Dimension of Inductance::
📅MOE 2011
Q31.
The coefficient of thermal conductivity is expressed in the unit
📅MOE 2010
Q32.
Dimension of Work is same as
📅KU 2014
Q33.
Which of the following pairs of physical quantities has the same dimension?
📅KU 2012
Q34.
The dimension of which of the following has \([ML^{-1}T^{-1}]\)
📅KU 2013
Q35.
Dimension of the stress
📅I.E. 2010
Q36.
Candela is the unit of
📅I.E. 2012
Q37.
1 Watt second is equal to
📅I.E. 2012
Q38.
Find out the dimension of K in the equation: \(W = 1/2 kx^{2}\)
📅I.E. 2013
Q39.
If energy E, velocity V and time T are taken as fundamental units, the dimensional formula for surface tension becomes
📅
Q40.
Which of the following system of units cannot enter into fundamental units?
📅
Q41.
What are the dimensions of angular displacement?
📅
Q42.
The position x of a particle at time t is given by \(x = b/a (1-e^{at})\) where a and b are non-zero constants. The dimensions of b are
📅
Q43.
In Vander Waal's equation \((P + a/V^2)(V-b) = RT\), the dimension of 'a' are
📅
Q44.
The unit of Stefan's Boltzmann contant \(\sigma\) is
📅
Q45.
Which of the following have same dimension
📅
Q46.
Which of the following is a correct unit of gravitational constant?
📅MOE-2009
Q47.
Dimension of Angstrom (A), Micron (μ), Fermi (F) and Nanometer (nm) is the same. Which one of the following represent the correct arrangement of their magnitude in the decreasing order?
📅MOE-2009
Q48.
S.I unit equivalent to the magnetic field Tesla (T) may be
📅MOE-2009
Q49.
The dimensional formula or coefficient of viscosity is
📅KU-2010/MOE
Q50.
\(NC^{-1} has the same dimension as\)
📅KU 2009
Q51.
The dimensional formula of impulse is
📅KU 2009
Q52.
The nearest star beyond the Sun is approximately 4 light-years away. The distance is:
Q53.
The dimensions of angular momentum are:
📅IOM 96
Q54.
The dimensional formula for stress is the same as that for
📅MOE 066
Q55.
Dimension of permittivity of free space \((\varepsilon_{0})\) is
📅MOE 2066
Q56.
The dimension of Universal Gravitational constant is
Q57.
The dimension of velocity gradient is the same as that of
📅MOE 2065
Q58.
If the units of force and length are doubled while the unit of time remains unchanged, the unit of power becomes:
📅MOE 2063
Q59.
The dimension \((M^{1}L^{2}T^{-2})\) refers to a physical quantity that has unit:
📅MOE 2063
Q60.
The dimensional formula for Plank's constant is
📅MOE 2063/ BP 2016
Q61.
The diameter of nucleus is of order of
📅MOE 2063
Q62.
The unit of \(\varepsilon_{o}\), the absolute permitivity of free space are
📅MOE 2062
Q63.
The dimension of current is:
📅MOE 2062
Q64.
The dimensional formula for kinetic energy is:
📅MOE 2010
Q65.
Which of the following have same dimension?
📅MOE 2061
Q66.
\([ML^2T^{-3}I^{-1}]\) is the dimensional formula of:
📅MOE 2056
Q67.
'Light year' is the unit of
📅MOE 2056
Q68.
The S.I. unit of electric field
📅IE 2007
Q69.
The dimensional of modulus of rigidity is:
📅BPKIHS - 08
Q70.
Weight of milky way galaxy is
Q71.
Which is not a unit of length?
📅BPKIHS 02
Q72.
The pair NOT having identical dimensions is:
📅BPKIHS-03
Q73.
The dimension of E/B is same as that of
📅BPKIHS-04
Q74.
If the current in electric bulb drops by one percent the power decreases by:
📅BPKIHS 05
Q75.
Which of the relation is correct from dimensional point of view?
📅BPKIHS-94
Q76.
The density of a material of a cube is calculated by measuring its mass and a side. What is the maximum percentage error in the density if the errors in the measurement of side and mass are 3% and 4% respectively.
📅BPKIHS 1995
Q77.
In Astronomy, there is a unit of distance called AU. The astronomical unit. This denotes the distance between
📅BPKIHS 1995
Q78.
The dimensional formula of surface tension is
Q79.
The term 'light year' is used for
Q80.
If the radius of earth were to decrease by 1%, its mass remaining the same, the acceleration due to gravity on the surface of the earth will
Q81.
Coefficient of viscosity (η) has the dimension \(Nm^{-2}S\). It is equivalent to
📅IOM 2015
Q82.
\(e^2/\varepsilon_0\) has dimension of
📅IOM 2016
Q83.
The unit of Resistance in SI system is
📅KU 2016
Q84.
The dimension \(ML^{-1}T^{-2}\) corresponds to:
📅KU 2017