Q 11-01-041JEE MainMedium
In a new system of units, the unit of mass is $2\ \text{kg}$, the unit of length is $5\ \text{m}$ and the unit of time is $10\ \text{s}$. Find the numerical value of an energy of $100\ \text{J}$ in this system.
Numerical value type. Enter your answer.
Answer: 200
Energy has dimensions $[ML^2T^{-2}]$, and $n_1 u_1 = n_2 u_2$:
$$n_2 = n_1\left(\frac{M_1}{M_2}\right)\left(\frac{L_1}{L_2}\right)^2\left(\frac{T_1}{T_2}\right)^{-2}$$
$$= 100\times\frac{1}{2}\times\left(\frac{1}{5}\right)^2\times\left(\frac{1}{10}\right)^{-2} = 100\times 0.5\times 0.04\times 100 = 200$$
The new unit of energy is smaller than a joule, so the number gets bigger.
Solution by Sreeraj P, M.Sc Physics