Q 11-01-215JEE MainJEE Main 2019 (10 Jan, Shift 1)Easy
The density of a material in SI units is $128\ \text{kg m}^{-3}$. In certain units in which the unit of length is $25\ \text{cm}$ and the unit of mass is $50\ \text{g}$, the numerical value of density of the material is:
Answer: (C) $40$
$n_1u_1 = n_2u_2$, with $u = \dfrac{\text{mass}}{\text{length}^3}$:
$$n_2 = 128\times\frac{1\ \text{kg}}{50\ \text{g}}\times\left(\frac{25\ \text{cm}}{1\ \text{m}}\right)^3 = 128\times20\times\frac{1}{64} = 40$$
Solution by Sreeraj P, M.Sc Physics