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 $5$cm and the unit of mass is $10g$?

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

Answer 1

The correct option is D $4.8\times {10}^5$

$I=12Kg{m}^2$

New system $\Rightarrow$ unit length $=5cm$ and unit mass $=10g$.

$I=12\times 1000\times \left({10}^4\right)g{cm}^2$

In $I$ unit length $=5cm$. unit mass $=10g$.

$I=12\times \frac{10000\times {10}^3}{25\times 10}\left(10g\right)\left(5{cm}^2\right)$

$I=48000\left(10g\right){\left(5cm\right)}^2$

$=4.8\times {10}^5$