Question

The moment of inertia of brass solid sphere about an axis passing through its centre is $1.6kg{m}^2$. The moment of inertia of another brass sphere of radius half of radius of the first sphere about its natural axis is:

• A. $0.5kg{m}^2$
• B. $0.1kg{m}^2$
• C. $0.05kg{m}^2$
• D. $0.01kg{m}^2$

Answer 1

The correct option is C $0.05kg{m}^2$

Let the mass of sphere be $M$

So $M=\frac{4\pi r^3\rho }{3}$

When the radius is halved we have $M_1=\frac{4\pi (r/2{)}^3}{3}=M/8$

$I=\frac{2M{r}^2}{5}=1.6$

$I_1=\frac{2M_1(r/2{)}^2}{5}=\frac{I}{32}=0.05kg{m}^2$