Question

Using dimensions convert
(a) $1$ newton into dynes
(b) $1$ erg into joules

Answer 1

Dimension of Joule is given as

$J=\frac{kg\cdot m^2}{s^2}$

$J=1\times {\left(\frac{M_1}{M_2}\right)}^1\times {\left(\frac{L_1}{L_2}\right)}^2\times {\left(\frac{T_1}{T_2}\right)}^{-2}$

$=1\times \left(1000\right)g\times {\left(100cm\right)}^2\times {\left(1s\right)}^{-2}$

$={10}^7$

Hence $1J={10}^{7}erg$

Similarly dimension of Newton is

$N=kg\frac{m}{{\sec }^2}$

$N=1\times {\left(\frac{M_1}{M_2}\right)}^1\times {\left(\frac{L_1}{L_2}\right)}^1\times {\left(\frac{1\sec }{1\sec }\right)}^{-2}$

$=1\times 1000g\times 100cm\times 1$

$={10}^{5}dyne$