Page 24 - Electrostatics-11

© GC Shiba
Measurement:

Unit: It is the standard reference used to measure a physical quantity.

Fundamental physical quantities: Mass(M), Length (L), time (T), electric
current (A), temperature (K), luminous intensity, amount of matter.

Dimension: Power raised to the fundamental units to express physical quantity.
E.g., M is the dimension of mass.

Dimensional formula: The physical quantity expressed in terms of basic units

0
with their proper power is called dimensional formula. E.g., [ −1 ] is the
dimensional formula of velocity.

Writing dimensional formula

0
Velocity (V) = = [ ] = [ −1 ] = −1
[ ]

Acceleration (a) = ℎ = [ −1 ] = [ −2 ]
[ ]

Force (F) = ma = [ ][ −2 ] = −2

−1 −2
Pressure (P) = = = −2 =
2

Surface tension = = −2 =
0 −2
ℎ

1
Frequency (F) = 1 = = −1

Taking force (F), length (L) and time (T) as a fundamental quantity, Obtain
the dimensional formula for density and gravitational constant (G).

−4 2
Density = = = = [ ] = [ ]
3
× [ −2 ][ ]
2
2 [ ][ ]
2
2
Gravitational constant (G) = = = [ −1 ][ ][ ]

2 [ ][ ]
1

2
= [ −1 ][ ][ −2 ] = [ −1 4 −4 ]

1 Mechanics