Question

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

Answer 1

Answer: 25

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