Question

A hollow sphere and a solid sphere, of equal mass and equal radii roll down without slipping on an inclined plane. If the torque experienced by the hollow sphere and solid sphere are $\tau_H$ and $\tau_S$ respectively, then

• A. $\tau_H < \tau_S$
• B. $\tau_H > \tau_S$
• C. $\tau_H = \tau_S$
• D. $\tau_H = 0$

Answer 1

Answer: (B)

$\tau_H > \tau_S$

Answer 2

As we know, moment of inertia of hollow
sphere $I_{H}=\frac{2}{3} M R^{2}$ and moment of inertia of solid
sphere $I_{S}=\frac{2}{5} M R^{2}$
$\therefore I_{H}>I_{S}$
Since, torque $=I \alpha$
$\Rightarrow$ Torque $\left(\tau_{H}\right)>$ Torque $\left(\tau_{S}\right)$