In a system, unit of mass is $A \mathrm{~kg}$, length is $B \mathrm{~m}$ and time is $C \mathrm{~s}$, then…

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
  1. $10 A^{-1} B^{-1} C^{-2}$
  2. $10 A^{-1} B^{-1} C^2$
  3. $10 A B C^{-2}$
  4. $5 A^{-1} B C^2$

Solution

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 $10 A^{-1} B^{-1} C^2$.

Asked in: AP EAMCET 2018 (22 Apr Shift 2)

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