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If the unit of force is $100 \mathrm{~N}$, unit of length is $10 \mathrm{~m}$ and unit of time is $100 \mathrm{~s}$, what is the unit of mass in this system of units?
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Verified Answer
As given that, $F=100 \mathrm{~N}, L=10 \mathrm{~m}$
As we know that,
Dimension of force $F=\left[\mathrm{MLT}^{-2}\right]=100 \mathrm{~N}$
Length $(L)=[\mathrm{L}]=10 \mathrm{~m}$
Time $(t)=[\mathrm{T}]=100 \mathrm{~s}$
Substituting values of $L$ and $T$ in eq. (1), we get $M \times 10 \times(100)^{-2}=100$
$$
\begin{aligned}
&\frac{M \times 10}{100 \times 100}=100 \\
&\text { So, } M=100 \times 1000 \mathrm{~kg} \\
&M=10^5 \mathrm{~kg} \\
&F=10^2 \mathrm{~N}
\end{aligned}
$$
Hence the unit of mass is $10^5 \mathrm{~kg}$.
As we know that,
Dimension of force $F=\left[\mathrm{MLT}^{-2}\right]=100 \mathrm{~N}$
Length $(L)=[\mathrm{L}]=10 \mathrm{~m}$
Time $(t)=[\mathrm{T}]=100 \mathrm{~s}$
Substituting values of $L$ and $T$ in eq. (1), we get $M \times 10 \times(100)^{-2}=100$
$$
\begin{aligned}
&\frac{M \times 10}{100 \times 100}=100 \\
&\text { So, } M=100 \times 1000 \mathrm{~kg} \\
&M=10^5 \mathrm{~kg} \\
&F=10^2 \mathrm{~N}
\end{aligned}
$$
Hence the unit of mass is $10^5 \mathrm{~kg}$.
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