Question

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

• A. $0.4$
• B. $40$
• C. $400$
• D. $0.04$

Answer 1

Answer: (B)

In the CGS system,
$d \, = \, 4 \, g \, cm^{- 3}$
The unit of mass is $100 \, g$ and unit of length is $10 \, cm$ , so
density $= \, \frac{4 \left(\right. \frac{100 \, g}{100} \left.\right)}{\left(\right. \frac{10}{10} \, cm \left.\right)^{3}}$
$= \, \frac{\left(\right. \frac{4}{100} \left.\right)}{\left(\right. \frac{1}{10} \left.\right)^{3}} \, \frac{\left(\right. 100 \, g \left.\right)}{\left(\right. 10 \, cm \left.\right)^{3}}$
$= \, \frac{4}{100} \, \times \, \left(\right. 10 \left.\right)^{3} \, \frac{100 \, g}{\left(\right. 10 \, cm \left.\right)^{3}}$
$= \, 40 \,$ units