Question

How many dynes are equal to $1\mathrm{N}$?

• A. ${10}^6$
• B. ${10}^4$
• C. ${10}^5$
• D. ${10}^3$

Answer 1

The correct option is C

${10}^5$

Step1: Definition

According to the second law of motion, force is the product of mass and acceleration, that is $\mathrm{Force}\left(\mathrm{F}\right)=\mathrm{Mass}\left(\mathrm{m}\right)\times \mathrm{Acceleration}\left(\mathrm{a}\right)$

Thus, the SI unit of force is $\mathrm{kg}\mathrm{m}/{\mathrm{s}}^2$ which is known as newton($\mathrm{N}$).

The CGS unit of force is $\mathrm{g}\mathrm{cm}/{\mathrm{s}}^2$ which is also called as dyne.

Step2: Finding a solution

Now,

$$\begin{gathered} 1\mathrm{N}=1\mathrm{kgm}/{\mathrm{s}}^2 \\ 1\mathrm{N}=\frac{1\mathrm{kg}\times 1\mathrm{m}}{{\sec }^2} \\ \mathrm{Since}, \\ 1\mathrm{kg}=1000\mathrm{g} \\ \mathrm{And},1\mathrm{m}=100\mathrm{cm} \\ \mathrm{Then}, \\ 1\mathrm{N}=\frac{1000\mathrm{g}\times 100\mathrm{cm}}{{\sec }^2} \\ 1\mathrm{N}=\frac{{10}^5\mathrm{gcm}}{{\sec }^2} \\ \mathrm{Thus}, \\ 1\mathrm{N}={10}^5\mathrm{gcm}/{\sec }^2 \\ \mathrm{But},\mathrm{gcm}/{\sec }^2=\mathrm{dyne} \\ \mathrm{Hence}, \\ \mathbf{1}\mathbf{N}\mathbf{=}{\mathbf{10}}^{\mathbf{5}}\mathbf{dyne} \end{gathered}$$

Thus,

Option c) ${\mathbf{10}}^{\mathbf{5}}$ is the correct option.