Question

Imagine a system of units in which the unit of mass is $10\, kg$, length is $1 \,km$ and time is $1 \,min$. Then 1 joule in this system is equal to

• A. $360$
• B. $3.6\times10^{-4}$
• C. $3.6\times10^{4}$
• D. $3.6$

Answer 1

Answer: (B)

$n_{1}u_{1}=n_{2}u_{2}$
$\Rightarrow { n _{2}}\left(\frac{n_{1}}{n_{2}}\right)u_{1}=\left(\frac{M_{1}}{M_{2}}\right)^{^1}\left(\frac{L_{1}}{L_{2}}\right)^{^2}\left(\frac{T_{1}}{T_{2}}\right)^{^{-2}}$
$u_{1}=\left(\frac{1\,kg}{10\,kg}\right)\left(\frac{1\,m}{1\,km}\right)^{2}\left(\frac{1\,s}{1\,min}\right)^{-2}\times1$
$=\frac{1}{10}\times10^{-6}\times60\times60$
$=36\times10^{-5}$
$=3.6\times10^{-4}$