Question

If a spherical ball rolls on a table without slipping the friction of its total energy associated with rotational energy is:

• A. 44625
• B. 44599
• C. 44597
• D. 44627

Answer 1

The Correct Option is B

Rotational energy of sphere
$E_{R}=\frac{1}{2} I \omega^{2}$
For sphere, moment of inertia
$I =\frac{2}{5} m R^{2}$
$\therefore E_{R} =\frac{1}{2}\left(\frac{2}{5} m R^{2}\right)\left(\frac{v}{R}\right)^{2}$
$=\frac{1}{5} m v^{2}$
Translational kinetic energy $E_{r}=\frac{1}{2} m v^{2}$
$\therefore$ Total energy $=\frac{1}{5} m v^{2}+\frac{1}{2} m v^{2}$
$=\frac{7}{10} m v^{2}$
$\therefore$ Required fraction
$=\frac{\frac{1}{5} m v^{2}}{\frac{7}{10} m v^{2}}$
$=\frac{2}{7}$