Question:
to convert a physical quantity from one system of units to another ex.G in cgs system is 6.67*10-8 dyne cm2 g-2 calculate its value in SI units
Answer:
In cgs system
G cgs = 6.67 × 10−8
M1 = 1g
L1 = 1 cm
T1 = 1s
In SI system
G = ?
M2 = 1 kg
L2 = 1m
T2 = 1s
The dimensional formula for gravitational constant is [M-1L3T-2]
In cgs system, dimensional formula for G is [M1xL1yT1z]
In SI system, dimensional formula for G is [M2xL2yT2z]
Here x = −1, y = 3, z = −2
[M2xL2yT2z] = Gcgs[M1xL1yT1z]
G = Gcgs[M1/m2]x[M1/m2]y[M1/m2]z
= 6.67 × 10−8 [1g/1kg]-1[1cm/1m]3[1s/1s]-2
= 6.67 × 10−11
In SI units,
G = 6.67 × 10−11 N m2 kg−2
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