This document discusses different methods of measurement of length, large distances, small distances, and mass. It describes direct and indirect methods of measuring length using instruments like meter scales and Vernier calipers. It then explains the parallax method for measuring large distances between planets and stars from Earth by observing the angle of parallax. For small distances, it discusses using the parallax angle relationship between the basis and distance. Formulas are provided for calculating distance based on parallax angle and basis. Measurement techniques for small masses include using unified atomic mass units since masses of atoms and molecules cannot be measured in kg.

1. UNIT AND MEASUREMENT
Class – 11th
Aditya Mishra
Email: adityakumar2009@gmail.com
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2. MEASUREMENT OF LENGTH
Measurement of length
Direct method
1 2
Indirect method
- Measurement of length using
measuring instruments such as
meter scale, Vernier caliper ,
Micro-meter
- Absolute measurement
- Measurement of length using
comparison with the standard
object E.g Dial gauge
- Comparative measurement
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3. 1. Parallax method :
- Indirect method
- Used to measure large distances
e.g. distance between planet and star from earth
MEASUREMENT OF LARGE DISTANCES
o
1 = 1 = 1 degree

2 = 1 = 1 minute
 
3
-6
= 1 = 1 second
= 4.85 × 10 rad
 
o
1 = 60
1 = 60
 
-6
-4
= 60 1
= 60 4.85 x 10 rad
= 2.908 10 rad




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4. WHAT IS PARALLAX?
• Change in the position of the object with respect to the background
when an object is seen from two different positions is called parallax
L L
R
Seen from left eye Seen from right eye
(a) (b)
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5. MEASUREMENT OF SMALL DISTANCES


O
P
Q
b (basis)

D
D
• Assuming the object is far away i.e. D >>>> b , b/D << 1 ,
• is very small
• arc PQ = straight line PQ s = b
S r 
 
b D 
 
b
D
 

Parallax
Angle
PQ = b
OP = OQ = D
POQ = 

s
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6. PROBLEM
Q.1 A moon is observed from two diametrically opposite points A and B on
Earth. The angle theta subtended at the moon on the two directions of
observation is 1o54/. The diameter of Earth is 1.267 x 107m. Compute the
distance of moon from earth ?
Ans : Given :
o
= 1 54
 
= (60 +54 )
= 114
 

-6
= 114 1
= 114 4.85 10 rad


 
-2
= 3.32 10 rad

7
d = 1.267 10 m

To Find :
Solution :
We know from the parallax method,
Paralytic angle
b
=
D

Distance between sun
and earth (D)
D θ = b
 
D =
b

7
2
1.276 10
=
3.32 10


7 2
1.276 10
=
3.32


8
D = 3.84 10 m

 
o
1 = 60
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7. MEASUREMENT OF SMALL DISTANCES
Mono-layer : single layer of molecules
t
Volume of the solution
t =
Area of the solution
n V
=
A
t = dimaeter of one molecule (d)
n = number of atoms present in
mono-layer
V = total volume of solution
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8. MEASUREMENT OF MASS
Measurement of very small masses:
• Mass of atoms and molecules cannot be measured in kg
• Unified atomic mass unit (u)
1
1 = of mass of carbon -12 ( including mass of electrons)
12
u
-27
1 = 1.66 10 kg
u 
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