Question

Two uniform spheres of mass M have radii R and 2R. Each sphere is rotating about a fixed axis through a diameter. The rotational kinetic energies of the spheres are identical. What is the ratio of the magnitude of the angular momenta of these spheres? That is, $\frac{L_{2R}}{L_R}=$

• A. 4
• B. $2\sqrt{2}$
• C. 2
• D. $\sqrt{2}$
• E. 1

Answer 1

Answer: (C)

2

The ratio of their angular momenta is given as:
$\frac{L_{2R}}{L_R}=\frac{I_1{\omega }_1}{I_2{\omega }_2}$ $=\frac{\frac{I_1{v}_1}{2R}}{\frac{I_2{v}_2}{R}}$
As the rotational kinetic energies of both the spheres is same we get $v_1=v_2$ and also the moment of inertia $I$ for a sphere is $I=\frac{2}{5}M{R}^2$
Substituting this, we get the ratio as $2$.