Question

Find the angular velocity of sphere just after impulse is applied.

• A. $\frac{2v_0}{R}$
• B. $\frac{v_0}{R}$
• C. $\frac{v_0}{2R}$
• D. $\frac{3v_0}{R}$

Answer 1

The correct option is A $\frac{2v_0}{R}$

$I\omega =m{v}_{0}R-\mu NdtR$
$Ndt=\frac{3}{5}m{v}_0$ , it is the vertical component of impulse. As $J>>mgdt$ we neglect it in normal force.
$\frac{2}{5}m{R}^2\omega =m{v}_{0}R-\frac{1}{3}.\frac{3}{5}m{v}_{0}R\Rightarrow \omega =\frac{2v_0}{R}$