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convert 1newton into dyne using dimensional analysis.

the 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]1x1
n2=1000×100 = 100000 = 105 dynes

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View Full Answer

Here, Newton is S.I. unit of force.

We know , the dimensional formula of force is ( M L T -2)

Let n 1 = number in S.I.

n2= number in C.G.S.

Then n1 (M1 L1 T1-2 ) = n2 (M2L2 T2 -2 )

or, 1 (1kg * 1m * 1s -2 ) = n2 ( 1g * 1cm * 1s -2 )

or, ( 1000g * 100cm * 1s -2 ) = n2 (1g * 1cm * 1s -2 )

or, n2 = 10 5

1 N = 10 5 dynes

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