Question

The moment of inertia of a body rotating about a given axis is $12.0kg{m}^2$ in the SI system. What is the value of the moment of inertia in a system of units in which the unit of length is $5cm$ and the unit of mass is $10g?$

• A. $2.4\times 10^3$
• B. $6.0\times 10^3$
• C. $5.4\times 10^5$
• D. $4.8\times 10^5$

Answer 1

Answer: (D)

$n_2=n_1{\left(\frac{M_1}{M_2}\right)}^a{\left(\frac{L_1}{L_2}\right)}^b{\left(\frac{T_1}{T_2}\right)}^c$
Dimensional formula of moment of inertia
$=\left[M{L}^2{T}^0\right]$
$\therefore a=1,b=2,c=0$
Here, $n_1=12.0,M_1=1kg,M_2=10g$
$L_1=1m,L_2=5cm,T_1=1s,T_2=1s$
$\therefore n_2=12.0{\left(\frac{1kg}{10g}\right)}^{1\cdot }{\left(\frac{1m}{5cm}\right)}^2{\left(\frac{1s}{1s}\right)}^0$
$=12\times {\left(\frac{1000g}{10g}\right)}^1{\left(\frac{100cm}{5cm}\right)}^2\times 1=12\times 100\times 400=4.8\times 10^5$