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In a system, unit of mass is $A \mathrm{~kg}$, length is $B \mathrm{~m}$ and time is $C \mathrm{~s}$, then the value of $10 \mathrm{~N}$ in this system is
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Verified Answer
The correct answer is:
$10 A^{-1} B^{-1} C^2$
Using,
$\begin{aligned}
\text {Using, } N_1 u_1 & =N_2 u_2 \\
10 \mathrm{~kg} \frac{\mathrm{m}}{\mathrm{s}^2} & =N_2\left(\frac{A \cdot B}{C^2}\right) \\
\Rightarrow N_2 & =\frac{10 \cdot C^2}{A \cdot B} \\
& =10 A^{-1} B^{-1} C^2
\end{aligned}$
So, numerical value of $10 \mathrm{~N}$ in given system is $10 A^{-1} B^{-1} C^2$.
$\begin{aligned}
\text {Using, } N_1 u_1 & =N_2 u_2 \\
10 \mathrm{~kg} \frac{\mathrm{m}}{\mathrm{s}^2} & =N_2\left(\frac{A \cdot B}{C^2}\right) \\
\Rightarrow N_2 & =\frac{10 \cdot C^2}{A \cdot B} \\
& =10 A^{-1} B^{-1} C^2
\end{aligned}$
So, numerical value of $10 \mathrm{~N}$ in given system is $10 A^{-1} B^{-1} C^2$.
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