Q84 / 120 · NEET 2011 (Mains) · Physics
The density of material in CGS system of units is $4 \mathrm{~g} / \mathrm{cm}^3$. In a system of units in which unit of lengths is $10 \mathrm{~cm}$ and unit of mass is $100 \mathrm{~g}$, the value of density of material will be
- A0.4
- Correct answerB40
- C400
- D0.04
Solution
Mass,
$$
\begin{aligned}
& M=d V \\
& d=\frac{M}{L^3} \\
& d=4 \mathrm{~g} / \mathrm{cm}^3
\end{aligned}
$$
If unit of mass is $100 \mathrm{~g}$ and unit of distance is $10 \mathrm{~cm}$.
So, density
$$
\begin{aligned}
y & =\frac{4\left(\frac{100 \mathrm{~g}}{100}\right)}{\left(\frac{10}{10} \mathrm{~cm}\right)^3} \\
& =\frac{\left(\frac{4}{100}\right)}{\left(\frac{1}{10}\right)^3} \cdot \frac{(100 \mathrm{~g})}{(10 \mathrm{~cm})^3} \\
& =40 \mathrm{~g} \mathrm{~cm}^{-3}
\end{aligned}
$$
Aliter
$$
\begin{aligned}
u_2 & =u_1\left(\frac{M_1}{M_2}\right)\left(\frac{L_1}{L_2}\right)^{-3} \\
& =4\left(\frac{1}{100}\right)\left(\frac{1}{10}\right)^{-3} \\
& =40
\end{aligned}
$$
Hence, the correct answer is option: 'B'.