Question

The moment of inertia of a body rotating about a given axis is $12.0$ kg$m^2$ in the SI system (let say $I$). What is the magnitude of the moment of inertia in a system of units in which the unit of length is equivalent to $5$ cm and the unit of mass is equivalent to $10$ g? Answer in new unit.

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

Answer 1

Answer: (D)

$4.8\times$${10}^5$

We need to convert $12kg{m}^2$ into given system of units.

It is $12\times 1000gm\times (100cm{)}^2$

But 10 gm is 1 mass unit (U) and 5 cm is one length unit (L).

Hence, =$12\times 100massunit\times (20lengthunit{)}^2$

= $4.8\times {10}^5$ $U{L}^2$