3 Units & Dimensions
Tunneling microscope:
1 Measurement of Length Mass
& time Uses quantum tunneling for atomic-level
objects.
Parallax Used to measure large Electron microscope:
Method distance
Uses electrons for high-resolution imaging.
p
Measurements:
Pa r a l l a x θ
x b Astronomical Unit (AU):
Angle =
x
Used to measure distances within our
b solar system.
Where, 1AU = 1.496 × 10
11
m
θ = The angle formed between two lines of Light year (Ly):
sight to an object when observed from two The distance that light travels in one year.
distinct positions. 15
1Ly = 9.46 × 10 m
b = The distance between the two observation
Parsec:
points
Another unit used in astronomy to
x = The actual distance to the object being
measure large distances.
measured
1parsec = 3.08 × 1016m
Note:
+ –15
Size of proton (P ) = 10 m (1 fermi)
The conversion between degrees, minutes,
–10
and seconds to radians helps in precise Size of an atom, = 10 m (1A°)
calculation and understanding of the small Radius of earth, REarth = 10 m
7
angles involved in parallax measurements.
Distance of boundary of
= 1026 m
1º = 60' = 1.745 × 10
-2
rad Observable Universe
-4
1΄ = 60' = 2.91 × 10 rad
2 Conversion of Units
-6
1˝ = 4.85 × 10 rad
nu = constant, n = measure value of Physical
Measuring Very Small Sizes:
quantity, u = unit of that Physical quantity.
Optical microscope: 1
n ∝
For small objects visible with light. u
, n nu 3 SI System (International
System of Units)
The SI (International System of Units) is a
modern version of the metric system, which
u u
is used worldwide for measuring different
n things. It is based on seven fundamental
units, called base units. Each base unit has a
specific symbol and represents a fundamental
quantity in science and everyday life. Here
1/u is a simple explanation of these base units,
their symbols, and what they measure:
→ Only use to find value of physical quantity
in new system of unit, if value is know in 7 Base/Fundamental Units:-
one unit.
No. Quantity Unit Symbol
Measurement of Mass & Time
1. Length Meter m
1 12
1 amu =
12 Mass of C atom 2. Mass Kilogram kg
1 amu = 1.66 × 10
-27
kg 3. Time Second S
–
e mass = 9.1 × 10-31 kg 4. Temperature Kelvin K
25
Earth mass:- 10 kg 5. Elec. Current Ampere A
55
Observable Universe =10 kg. 6. Luminous Candela cd
Intensity
Q.1. Convert 18 km/hr in m/s. s
7. Amt. of Sub Mole Mol
Sol. n1u1 = n2u2
2 supplementary Units:-
18 km/hr = n2 m/s
No. Quantity Unit Symbol
18 × 10 3 m
= n 2 m/s 1. Plane Angle radian rad
60 × 60s
5 2. Solid Angle Steradian sr
n 2 = 18 × =5
18 Plane Angle
Q.2. If unit of length is y m in new system of It is the ratio of the arc length (ds) to the
unit then find value of x m2 area in new radius (r) of the circle. It is measured in
system of unit. radians, which is a dimensionless unit.
Sol. un = cost
r ds
n1u1 = n2u2
dθ
x m2 = n2y2m2
o
x ds
n2 =
y 2 dθ =
r
25
Units & Dimensions
Tunneling microscope:
1 Measurement of Length Mass
& time Uses quantum tunneling for atomic-level
objects.
Parallax Used to measure large Electron microscope:
Method distance
Uses electrons for high-resolution imaging.
p
Measurements:
Pa r a l l a x θ
x b Astronomical Unit (AU):
Angle =
x
Used to measure distances within our
b solar system.
Where, 1AU = 1.496 × 10
11
m
θ = The angle formed between two lines of Light year (Ly):
sight to an object when observed from two The distance that light travels in one year.
distinct positions. 15
1Ly = 9.46 × 10 m
b = The distance between the two observation
Parsec:
points
Another unit used in astronomy to
x = The actual distance to the object being
measure large distances.
measured
1parsec = 3.08 × 1016m
Note:
+ –15
Size of proton (P ) = 10 m (1 fermi)
The conversion between degrees, minutes,
–10
and seconds to radians helps in precise Size of an atom, = 10 m (1A°)
calculation and understanding of the small Radius of earth, REarth = 10 m
7
angles involved in parallax measurements.
Distance of boundary of
= 1026 m
1º = 60' = 1.745 × 10
-2
rad Observable Universe
-4
1΄ = 60' = 2.91 × 10 rad
2 Conversion of Units
-6
1˝ = 4.85 × 10 rad
nu = constant, n = measure value of Physical
Measuring Very Small Sizes:
quantity, u = unit of that Physical quantity.
Optical microscope: 1
n ∝
For small objects visible with light. u
, n nu 3 SI System (International
System of Units)
The SI (International System of Units) is a
modern version of the metric system, which
u u
is used worldwide for measuring different
n things. It is based on seven fundamental
units, called base units. Each base unit has a
specific symbol and represents a fundamental
quantity in science and everyday life. Here
1/u is a simple explanation of these base units,
their symbols, and what they measure:
→ Only use to find value of physical quantity
in new system of unit, if value is know in 7 Base/Fundamental Units:-
one unit.
No. Quantity Unit Symbol
Measurement of Mass & Time
1. Length Meter m
1 12
1 amu =
12 Mass of C atom 2. Mass Kilogram kg
1 amu = 1.66 × 10
-27
kg 3. Time Second S
–
e mass = 9.1 × 10-31 kg 4. Temperature Kelvin K
25
Earth mass:- 10 kg 5. Elec. Current Ampere A
55
Observable Universe =10 kg. 6. Luminous Candela cd
Intensity
Q.1. Convert 18 km/hr in m/s. s
7. Amt. of Sub Mole Mol
Sol. n1u1 = n2u2
2 supplementary Units:-
18 km/hr = n2 m/s
No. Quantity Unit Symbol
18 × 10 3 m
= n 2 m/s 1. Plane Angle radian rad
60 × 60s
5 2. Solid Angle Steradian sr
n 2 = 18 × =5
18 Plane Angle
Q.2. If unit of length is y m in new system of It is the ratio of the arc length (ds) to the
unit then find value of x m2 area in new radius (r) of the circle. It is measured in
system of unit. radians, which is a dimensionless unit.
Sol. un = cost
r ds
n1u1 = n2u2
dθ
x m2 = n2y2m2
o
x ds
n2 =
y 2 dθ =
r
25
Units & Dimensions
