Question

The masses of two solid spheres of same material are in the ratio $\sqrt{2}:4$ . About an axis passing through the centre of small sphere, the moment of inertia is $I$ . The moment of inertia of larger sphere is:

• A. $2I$
• B. $2\sqrt{2}I$
• C. $4I$
• D. $4\sqrt{2}I$

Answer 1

The correct option is D $4\sqrt{2}I$

Given ratio of masses $m_1:m_2=\sqrt{2}:4$

$butmass=\rho V\Rightarrow m\propto r^3$

$\therefore r_1^3:r_2^3=1:2\sqrt{2}$

$\Rightarrow r_1:r_2=1:\sqrt{2}$

$\therefore ratioofmomentofInertia=\frac{m_1}{m_2}{\left(\frac{r_1}{r_2}\right)}^2$

$=\frac{\sqrt{2}}{4}{\left(\frac{1}{\sqrt{2}}\right)}^2$

$\frac{I}{I_l}=\frac{1}{4\sqrt{2}}$

$\Rightarrow I_l=4\sqrt{2}I$