Question

Convert 1 newton into dyne using dimensional analysis

Answer 1

Dimensional formula of Force F [M1 L1 T-2]

So a =1, b=1, c=-2
Now because Newton is in m.k.s system,We Have.
M1 = 1kg, L1 = 1m, T1 = 1s
M2 = 1g, L2 = 1cm, T2 = 1s

n1= 1 Newton
n2 = ?
Using the formula
n2= n1[M1/M2]a [L1/L2]b [T1/T2]c


n2= 1 [1kg/1g]1 [1m/1cm]1 [1s/1s]-2

n2= 1[1000g/1g]1 [100cm/1cm]1 x1
n2= 1000×100 = 100000
= 105 dynes

Answer 2

The correct answer is 10 the power 5 N

Proof: mks/cgs

1kg/1g 1m/g sec/sec

second also in second no change it will cancel

(1000gm/1gm) (100gm/1gm) (60sex/60sec)

1000x100x1

100000

We can say that

1 dyne is equal to 10 the power 5 Newton

Thank you