Question

Convert 1 dyne into newton using dimensional analysis

Answer 1

check the attached image:-

Answer 2

Answer:

Using dimensional analysis, 1 dyne = $\bold{10^{-5} \mathrm{N}}$

Explanation:

To convert 1 dyne into newton follow the below step by step process

1 dyne= x newton

The dimensional form of the above expression

$H_{1}^{1} L_{1}^{1} T_{21}=x H_{1}^{2} L_{1}^{2} T_{22}$

To find the value of x

$x=1 \times\left[\frac{H_{1}}{H_{2}}\right]^{1}\left[\frac{L_{1}}{L_{2}}\right]^{1}\left[\frac{T_{1}}{T_{2}}\right]^{2}$

$X=1 \times[g m / k g][c m / m][S / S]$

Convert the value of kg into gm and m into cm and cancel the common terms

$\mathrm{X}=1 \times[\mathrm{gm} / 1000 \mathrm{gm}][\mathrm{cm} / 100 \mathrm{cm}] 1$

$X=1 \times\left[\frac{1}{10^{3}}\right]\left[\frac{1}{10^{2}}\right] \times 1$

$\begin{array}{l}{X=\frac{1}{10^{5}}} \\ {=10^{-5}}\end{array}$

1 dyne = $\bold{10^{-5} \mathrm{N}}$