Question

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 1

To convert a measured value from one system to another system, we use
$N_1{u}_1=N_{2}u2$
Where, $N$ is numeric value and $u$ is unit.
We get
$128\frac{\text{kg}}{{\text{m}}^3}=N_2\frac{50g}{(25\text{cm}{)}^3}$
$[\because \text{density}=\frac{\text{mass}}{\text{volume}}]$
$\Rightarrow \frac{128\times 1000\text{g}}{100\times 100\times 100{\text{cm}}^3}=\frac{N_2\times 50\text{g}}{25\times 25\times 25{\text{cm}}^3}$
$\Rightarrow N_2=\frac{128\times 1000\times 25\times 25\times 25}{50\times 100\times 100\times 100}=40$

Why this question? JEE- There are some straight forward questions in JEE Mains. This one is not to be missed.