Question

convert 1 newton into dyne using dimensional analyais

Answer 1

1 newton is equal to 100000 dyne

Answer 2

1N = kgm/s^2

dyne belongs to CGS system
so,

It would change in the following way,

1 kg = 1,000g
and
1 m = 100 cm

so,
newton = kg.m/s^2 becomes
1000g.100cm/s^2 in CGS system which nothing else but dyne

1 dyne = 100,000 g.cm/s^2

so,

the ratio of newton to dyne is

1 : 100,000

so,
1 newton = 100,000 dyne