Question

The density of a material in CGS system of units is $4g/c{m}^3$. In a system of units in which unit of length is $10cm$ and unit of mass is $100g$, the value of density of material will be :

• A. $0.4$ Unit
• B. $40$ Unit
• C. $4400$ Unit
• D. $0.04$ Unit

Answer 1

The correct option is B $40$ Unit

In CGS, $d=4\frac{g}{{cm}^3}$

If unit of mass is $100g$, 4 g mass in new units is $\frac{4}{100}$ units

and unit of distance is $10cm$, 1 cm in new units is $\frac{1}{10}$ units

So, density $=\frac{4\left(\frac{g}{100}\right)}{{\left(\frac{1}{10}cm\right)}^3}$$=\frac{\left(\frac{4}{100}\right)}{{\left(\frac{1}{10}\right)}^3}=40units$