Question

A solid sphere is set into motion on a rough horizontal surface with a linear speed $v$ in the forward direction and an angular speed $\frac{v}{R}$ in the anticlockwise direction as shown in figure. Find the linear speed of the sphere when it stops rotating and $\omega =\frac{v}{R}$.

• A. $\frac{3v}{5}$
• B. $\frac{2v}{5}$
• C. $\frac{4v}{3}$
• D. $\frac{7v}{3}$

Answer 1

Answer: (A)

$\frac{3v}{5}$

Conserving angular momentum about the point on ground:
$m{v}_{0}R+I{\omega }_0=mVR+I\omega \Rightarrow mvR-\frac{2}{5}m{R}^2\frac{v}{R}=mVR+\frac{2}{5}m{R}^2\frac{V}{R}\Rightarrow \frac{3}{5}mvR=\frac{7}{5}mVR\Rightarrow V=\frac{3}{7}v$