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NEET 2011
Exam
NEET
Year
2011
Subject
Physics
Chapter
Units and Dimensions

NEET 2011 · Physics · Units and Dimensions

The density of material in CGS system of units is 4 ~g / cm^3 . In...

The density of material in CGS system of units is 4 g/cm34 \mathrm{~g} / \mathrm{cm}^3. In a system of units in which unit of lengths is 10 cm10 \mathrm{~cm} and unit of mass is 100 g100 \mathrm{~g}, the value of density of material will be

Options

  1. A0.4
  2. B40
  3. C400
  4. D0.04

Correct answer

B. 40

Step-by-step solution

Mass, M=dVd=ML3d=4 g/cm3\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 g100 \mathrm{~g} and unit of distance is 10 cm10 \mathrm{~cm}. So, density y=4(100 g100)(1010 cm)3=(4100)(110)3⋅(100 g)(10 cm)3=40 g cm−3\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 u2=u1(M1M2)(L1L2)−3=4(1100)(110)−3=40\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}
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