Question

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

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

Answer 1

The Correct Option is C

To solve this problem, we need to convert the given density of the material from the CGS system to a new system of units where the unit of length is 10\,cm and the unit of mass is 100\,g.

In the CGS system, the unit of density is g/cm^3. We are given that the density is 4\,g/cm^3.

We will follow these steps to convert the density:

1. Determine the conversion factor for length and mass:
   • In the new system, 1 unit of length is 10\,cm. Therefore, 1\,cm = \frac{1}{10} units of length.
   • In the new system, 1 unit of mass is 100\,g. Therefore, 1\,g = \frac{1}{100} units of mass.
2. Express the density in terms of the new system units:
   • The density in the new system is \frac{\text{mass (in new unit)}}{\text{volume (in new unit)}} = \frac{\text{mass (in g)} \times \frac{1}{100}}{\left(\text{volume (in }\mathit{cm}\right) \times \left(\frac{1}{10}\right)^3}.
3. Substitute the given density:
   • The volume conversion factor is (10)^3 = 1000, since volume is the cubed quantity of length.
   • We substitute into the formula: 4 \frac{g}{cm^3} \times \frac{\frac{1}{100}}{\frac{1}{1000}} = 4 \times 10.
   • Simplifying this, the density becomes 40 in the new units.

Therefore, the value of the density of the material in the new system of units is 40.