the value of G in c.g.s. system is 6.67*10-8dyne cm2/g2.what is its value in s.i.

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 The S. I value is 6.67 * 10-11 N m2 / kg2

The conversion

Let

In CGS system       In SI system

M1 = 1 g                 M2 = 1 kg

L1 = 1 cm               L2 = 1 m

T1 = 1 s                   T2 = 1 s

The dimensional formula for gravitational constant is [M-1L3T-2]

In CGS system the dimensional formula is [ M1xL1yT1z]

In SI system the dimensional formula is [M2xL2yT2z]

x = -1 , y = 3 and z = -2

G [M2xL2yT2z] = Gcgs  [ M1xL1yT1z]

G = Gcgs  [M1/M2]x   [L1/L2]y    [T1/T2]z

G = 6.67 * 10-8 [ 1g/1kg]-1   [1cm/1m]3   [1s/1s]-2

G = 6.67 * 10-8 [1g/1000g]-1  [1cm/100cm]3   [1]-2

G = 6.67 * 10-11

So in SI unit,

G = 6.67 * 10-11 N m2 / kg2

 

Hope , it helps you......

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