Question

(a) The unit of coefficient of viscosity in `CGS` system is poise `(g//cm .s)` Convert it into `SI` unit.
(b) The SI unit of work is joule, convert it into `CGS` unit.

Answer 1

The dimension of coeficient of viscosity is `[ML^(-1) T^(-1)]`
1 poise `= 1 g//m.s`
`SI` unit `= 1 kg//m.s`
`(SI u ni t)/(1 poise) = ((1 kg)/(1 g)) ((1 m)/(1 cm))^(-1) ((1s)/(1s))^(-1)`
`= ((1000)/(1 g)) ((100 cm)/(1 cm))^(-1) ((1s)/(1s))^(-1)`
`= 1000 xx ((1)/(100)) = 10`
`1 poise = (1)/(10) SI unit`
`= (1)/(10) kg//m.s`
(b) Dimensionally, energy : `[ ML^(2) T^(2)]`
`(1 j o u l e)/(1 erg) = ((1 kg)/(1g)) ((1 m)/(1 cm))^(2) ((1s)/(1s))^(-2)`
`= ((1000 g)/(1 g)) ((100 cm)/(1 cm))^(2)`
`= 1000 xx (100)^(2) = 10^(7)`
`1 j o u l e = 10^(7) erg`