Chemistry: Molecular Approach (4th Edition)

$\underline{1\text{ cm}}$
The relationship between the dyne and newton is as follows: $1\text{ dyne}={{10}^{-5}}\text{ N}$ One newton is the force that produces a uniform acceleration of 1 meter per square second, when acting on a body of 1 kg mass. So, $1\text{ dyne}=\left( 1\text{ kg} \right)\left( 1\text{ m/}{{\text{s}}^{2}} \right){{10}^{-5}}$ Now, $1\text{ kg}=1000\text{ g}$ and $1\text{ m}=100\text{ cm}$. Thus, \begin{align} & 1\text{ dyne}=\left( 1000\text{ g} \right)\left( 100\text{ cm/}{{\text{s}}^{\text{2}}} \right){{10}^{-5}} \\ & =\left( 1\text{ g} \right)\left( 1\text{ cm/}{{\text{s}}^{\text{2}}} \right) \end{align} Thus, the unit of length used to define dyne is a centimeter. The unit of length in dyne is $\underline{1\text{ cm}}$. One dyne is the force that when applied on a mass of 1 g produces a uniform acceleration of 1 centimeter per square second.