Page 28 - Electrostatics-11

© GC Shiba

1
1
1
Then, = ( ) ( ) ( )
1
2
2 2 2
1 1 1 1 1 −2
= 5 ( ) ( ) ( )
1 1 1

1000 1 100 1
= 5 ( ) ( ) × 1
1 1

5
= 5 × 10

iv. To determine the dimension of proportionality constant:
The force of attraction between two bodies is separated by certain distance is

given by ∝ 1 2
2
2
1
= ℎ .
2

2
, = … … … ( )
2
1

From above relation, we can say that dimension of 2 is the dim. of G.
2
1

0
0 2
∴, = 2 = [ −2 ][ ] = [ −1 3 −2 ]

2 [ ] 2
1

Limitations of dimensional analysis:
❖ Dimensionless constant can’t be determined by using dimensional analysis.
❖ Trigonometric and exponential relation can’t be derived using dimensional

analysis.
❖ Dimensional analysis can’t be used if the physical quantity involves other

quantities than mass, length and time.
❖ Dimensional analysis can’t be used to derive a relation if more than one term
is involved.
❖ It never gives numerical values (it confined to MLT only).

❖ It never provides the information whether the given quantity is vector or
scalar.

5 Mechanics