The density of a material in CGS system is 4 text g/cm ^3. In a new system where the unit of length is 10 cm and unit of mass is 100 g, what will be the numerical value of the density in the new system?

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NEET Physics QUESTION #7226

Question 1

The density of a material in CGS system is $4\ \text{g/cm}^3$. In a new system where the unit of length is 10 cm and unit of mass is 100 g, what will be the numerical value of the density in the new system?

0.04
0.4
40✔️
400

Correct Answer Explanation

Density $\rho = 4\ \text{g/cm}^3$. We need to convert this to the new unit system.

New unit of mass: $100\ \text{g}$, New unit of length: $10\ \text{cm}$

New unit of density $= \dfrac{100\ \text{g}}{(10\ \text{cm})^3} = \dfrac{100\ \text{g}}{1000\ \text{cm}^3} = 0.1\ \text{g/cm}^3$

Numerical value in new system $= \dfrac{4\ \text{g/cm}^3}{0.1\ \text{g/cm}^3} = 40$

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