Question

Two point size bodies of masses $2kg$, $3kg$ are fixed at two ends of a light rod of length $1m$. The moment of inertia of two bodies about an axis perpendicular to the length of rod and passing through centre of mass of two bodies is:

• A. $0.6kg{m}^2$
• B. $0.8kg{m}^2$
• C. $1kg{m}^2$
• D. $1.2kg{m}^2$

Answer 1

The correct option is D $1.2kg{m}^2$

The position of COM from $2kg$ mass is $3\times 1/(2+3)=0.6m$

So MI of $2kg$ mass about COM is $2\times {0.6}^2=0.72kg{m}^2$

and MI of $3kg$ mass about COM is $3\times {0.4}^2=0.48kg{m}^2$

So total MI is $0.72+0.48=1.2kg{m}^2$