Page 27 - Electrostatics-11

© GC Shiba
Comparing the dimensions from both sides,

1 1
= 0, = − , =
2 2
Putting the value of a, b, c in eq (i), we get

0 −1/2
= 1/2
1/2
, =
1/2

, = √

Experimentally value of k is found to be 2

∴, = 2 √

iii. To convert a physical quantity from one system into another system of

units.

For this, we use the relation
1 1= 2 2

Here, = numerical values = units in two systems
1 2
1 2

× [ ] = × [ ]
2
1
2
1 1
2
2
1
1 1 1
, = ( ) ( ) ( )
1
2
2 2 2
E.g.: Convert 5 N into dyne.
In S.I. system (given system) In CGS system (new system)
M1= 1 kg M2= 1 g
L1=1 m L2=1 cm
T1= 1 sec T2= 1 sec

n1=5 n2=?
Here, given physical quantity is force. So, it’s dimensional formula for force

[F]= [ −2 ]. ∴, = 1, = 1, = −2

4 Mechanics