Question

The moment of inertia of a body rotating about a given axis is $12.0 kg m ^{2}$ 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 $5 cm$ and the unit of mass is $10 g ?$

• 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
$=\left[ ML ^{2} T ^{0}\right]$
$\therefore a=1, b=2, c=0$
Here, $n_{1}=12.0, M_{1}=1 kg , M_{2}=10 g$
$L_{1}=1 m , L_{2}=5 cm , T_{1}=1 s , T_{2}=1 s$
$\therefore n_{2}=12.0\left(\frac{1 kg }{10 g }\right)^{1 \cdot}\left(\frac{1 m }{5 cm }\right)^{2}\left(\frac{1 s }{1 s }\right)^{0}$
$=12 \times\left(\frac{1000 g }{10 g }\right)^{1}\left(\frac{100 cm }{5 cm }\right)^{2} \times 1=12 \times 100 \times 400=4.8 \times 10^{5}$