Answer
\[\underline{1\text{ cm}}\]
Work Step by Step
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.
