Question

A boy is pushing a ring of mass $2kg$ and radius $0.5m$ with a stick as shown in the figure. The stick applies a force of $2N$ on the ring and rolls it without slipping with an acceleration of $0.3m/s^2$. The coefficient of friction between the ground and the ring is large enough that rolling always occurs. Then the coefficient of friction between the stick and the ring is

• A. $0.4$
• B. $0.8$
• C. $0.2$
• D. $0.5$

Answer 1

Answer: (A)

As $2-f_1=Ma$
$f_1=2-Ma=2-2\times 0.3=1.4N$
Taking torque about $C$
$f_{1}R-f_{2}R=I_c\alpha$
$\left(f_1-f_2\right)R=M{R}^2\frac{a}{R}\left(\because \alpha =\frac{a}{R}\right)$
$f_1-f_2=Ma$
$f_2=f_1-Ma=1.4-2\times 0.3$
$=0.8N$
$f_2=2\mu$
$\mu =\frac{0.8}{2}=0.4$