Question

A bowling ball rolis without slipping down an inclined plane inclined at an angle $\theta$ to the horizontal, as shown. The coefficient of static friction between the ball and the surface is $\mu_s$, and the coefficient of kinetic friction is $\mu_k$. What is the magnitude of the force of friction acting on the ball?

• A. zero
• B. $\mu_s m g \cos \theta$
• C. $\mu_s \frac{7}{5} m g \sin \theta$
• D. $\frac{2}{7} m g \sin \theta$

Answer 1

Answer: (D)

$m g \sin \theta-f=m a_{ cm }$
$f R=\frac{2}{5} M R^2 \alpha$
(torque $=I \alpha$ about COM $)$
$a_{ cm }=R \alpha \Rightarrow f=\frac{2 m g \sin \theta}{7}$