Question

In a new system of units, the unit of mass is $100 \,g$, unit of length is $4 \,m$ and unit of time is $2\, s$. The numerical value of $10\, J$ in this system is ___.

Answer 1

[Energy] $=M L^{2} T^{-2}$
In new system
$1$ unit of energy
$=\frac{(1 \text { unit mass })(\text { 1unit length })^{2}}{(1 \text { unit time })^{2}}=\frac{\left(\frac{100}{1000} kg \right)^{(4 m )^{2}}}{(2 \sec )^{2}}$
$=\frac{4}{10} kgm ^{2} / s ^{2}=\frac{4}{10} J$
Now $\frac{4}{10} J =1$ unit energy in new system
$10\, J =\frac{100}{4}$ unit $=25$ units