A boy is pushing a ring of mass 2kg and radius 0.3m with a stick as shown. The ring rolls without slipping on the ground with a linear acceleration of $0.4 m / s^{2}$ . The coefficient of friction between the stick and the ring is 0.6. Find (in newton), the normal component of force which the stick applies on the ring

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Detailed Solution

Let N be the normal component of force applied by stick on the ring. Let a and $α$ be acceleration and angular acceleration of ring.
FBD of ring
Question Image
Along horizontal
$N - \ln = m a$ ……(i)
Torque about centre of ring $= l α$
$\Rightarrow (f r_{1} - μ N) R = M R^{2} α$
Also $a = α R$
So $(f r_{1} - μ N) = M a$ ….. (ii)
Solving (i) and (ii)
$N = \frac{2 M a}{1 - μ} = \frac{0.8 \times 2}{0.4} = 4 N$

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