Question

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

• A. $360$
• B. $3.6\times 10^{-4}$
• C. $3.6\times 10^4$
• D. $3.6$

Answer 1

Answer: (B)

$n_1{u}_1=n_2{u}_2$
$\Rightarrow n_2\left(\frac{n_1}{n_2}\right)u_1={\left(\frac{M_1}{M_2}\right)}^{{}^1}{\left(\frac{L_1}{L_2}\right)}^{{}^2}{\left(\frac{T_1}{T_2}\right)}^{{}^{-2}}$
$u_1=\left(\frac{1kg}{10kg}\right){\left(\frac{1m}{1km}\right)}^2{\left(\frac{1s}{1min}\right)}^{-2}\times 1$
$=\frac{1}{10}\times 10^{-6}\times 60\times 60$
$=36\times 10^{-5}$
$=3.6\times 10^{-4}$