Question

A cylinder of mass m and radius r rolls down a circular track from point A as shown in the figure. Assume that the friction is just sufficient to support the rolling. Velocity of the cylinder at point A was zero. Assume r ≪ R. The reaction by the track on the cylinder at point B is

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

Answer 1

The correct option is A

$\frac{7}{3}mg$

From WET, $mgR=\frac{1}{2}m{v}^2(1+\frac{k^2}{r^2})\Rightarrow \frac{3}{4}\frac{m{v}^2}{R}=mg$ as $\frac{k^2}{r^2}=\frac{1}{2}$ and $N=mg+\frac{m{v}^2}{R}=mg+\frac{4mg}{3}$