Question

The moment of inertia of a solid sphere about an axis passing through its centre is $0.8kg{m}^2$. The moment of inertia of another solid sphere whose mass is same as the mass of first sphere but the density is eight times the density of first sphere, about an axis passing through its centre is :

• A. $0.1kg{m}^2$
• B. $0.2kg{m}^2$
• C. $0.4kg{m}^2$
• D. $0.5kg{m}^2$

Answer 1

The correct option is B $0.2kg{m}^2$

Mass is same $\Rightarrow V_1{\rho }_1=V_2{\rho }_2$

$\Rightarrow \left(\frac{4}{3}\pi R_1^3\right){\rho }_1=\left(\frac{4}{3}\pi R_2^3\right){\rho }_2$

${\rho }_2=8{\rho }_1$

$\Rightarrow R_1=2R_2$

Given,

Moment of inertia, $I$ = $\frac{2}{5}M{R}_1^2=0.8$

$\therefore \frac{2}{5}M{R}_2^2=\frac{2}{5}\frac{M{R}_1^2}{4}=\frac{0.8}{4}=0.2kg{m}^2$