Using dimensional analysis show that
(i) 1 J = $10^{7}$ erg
(ii) 1 N = $10^{5}$ dyne

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Solution

$(i) 1 J = 1 k g m^{2} s^{- 2} = 1000 g \times (100 c m)^{2} \times s^{- 2}$
$= 10^{7} g c m^{2} s^{- 2}$
$= 10^{7} e r g$

$(i i) 1 N = 1 k g m s^{- 2} = 1000 g \times (100 c m) \times s^{- 2}$
$= 10^{5} g c m s^{- 2}$
$= 10^{5} d y n e$

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