Question

On a rough horizontal floor four objects are rolling without slipping. They are i) a solid sphere ii) a hollow spherical shell iii) a solid cylinder iv) a hollow cylinder. If all of them have the same mass and linear velocity for their centres of mass, which object has more kinetic energy?

• A. Solid sphere
• B. Hollow spherical shell
• C. Solid cylinder
• D. Hollow cylinder

Answer 1

The correct option is D

Hollow cylinder

Kinetic energy of a rolling body body on a rough horizontal floor is given by K.E = $\frac{1}{2}$ $I_c$ $w^2$ + $\frac{1}{2}$ M ${v_{cm}}^2$

$\Rightarrow$ K.E = $\frac{1}{2}$ $I_c$ $\frac{{v_{cm}}^2}{R^2}$ = M ${v_{cm}}^2$ $v_{cm}$

As mass and $v_{c}m$ are constant for four objects,

$\Rightarrow$ K.E $\alpha$ $\frac{I_c}{R^2}$ $\Rightarrow$ K.$E_{solidshere}=\frac{2}{5}$ $\frac{M{R}^2}{R^2}$ = 0.4M

$\Rightarrow$ K.$E_{solidcylinder}=\frac{M{R}^2}{{2R}^2}$ = 0.5M

$\Rightarrow$ K.$E_{Hollowcylinder}=\frac{M{R}^2}{R^2}$ = 1M

$\therefore$ K.E of hollow cylinder is more among the given four objects.