Question

Two brass solid spheres have radii in the ratio $1:2$. About the axis passing through their centres, the ratio of thier moments of inertia of is:

• A. $1:4$
• B. $1:8$
• C. $1:16$
• D. $1:32$

Answer 1

Answer: (D)

$1:32$

Ratio of radii = $1:2$
$mass=\rho V\Rightarrow m\propto v=r^3$
$\therefore \frac{m_1}{m_2}={\left(\frac{r_1}{r_2}\right)}^3=\frac{1}{8}$
$\therefore$ Ratio of moment of inertia is $\frac{M_1}{M_2}{\left(\frac{R_1}{R_2}\right)}^2$

$=\frac{1}{8}{\left(\frac{1}{2}\right)}^2=\frac{1}{32}$