Question

A boy is pushing a ring of mass $2\, kg$ and radius $0.5 \,m$ with a stick as shown in the figure. The stick applies a force of $2\, N$ on the ring and rolls it without slipping with an acceleration of $0.3 \,m/s^2$. 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 = 1.4\, N $
Taking torque about $C$
$ f_{1}R - f_{2}R = I_{c} \alpha $
$ \left(f_{1} -f_{2}\right)R = MR^{2} \frac{a}{R} \quad\left(\because\alpha = \frac{a}{R}\right) $
$f_{1} -f_{2} = Ma$
$ f_{2} = f_{1} -Ma = 1.4 -2 \times 0.3$
$ = 0.8 \,N $
$ f_{2} = 2 \mu $
$ \mu = \frac{0.8}{2} = 0.4 $