Question

In S.I. system, gravitational unit of moment is kilogram force metre, (kgf-m). One kgf-m in C.G.S. system is equal to:

विकल्प

• 9.8 × 10⁷ dyne-cm

• 9.8 × 10⁸ dyne-cm

• 9.8 × 10⁶ dyne-cm

• none of these

Answer 1

9.8 × 10⁷ dyne-cm

Explanation:

We know that:

\[ 1\ \mathrm{kgf\text{-}m} = 9.8\ \mathrm{N\text{-}m} \quad \text{(since } 1\ \mathrm{kgf} = 9.8\ \mathrm{N}\textit{)} \]

Now, to convert N-m into dyne-cm, we break down the units:

\[ 1\ \text{Newton}\ (\mathrm{N}) = 10^{5}\ \mathrm{dyne} \]

\[ 1\ \text{metre}\ (\mathrm{m}) = 10^{2}\ \mathrm{cm} \]

Therefore:

\[ 1\ \mathrm{N\text{-}m} = 10^{5}\ \mathrm{dyne} \times 10^{2}\ \mathrm{cm} = 10^{7}\ \mathrm{dyne\text{-}cm} \]

Substituting this value back into the first equation:

\[ 1\ \mathrm{kgf\text{-}m} = 9.8 \times 10^{7}\ \mathrm{dyne\text{-}cm} \]