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/s2. The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is \left(\right. \frac{P}{10} \left.\right). The value of P is :

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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/s². The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is $(\frac{P}{10})$ . The value of P is :

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2 – f₂ = Ma_cm …….(1)

f₂ = 2 – 2 × 0.3 = 1 .4 N

(f₂ – f₁) R = I_cm $α$

$(f_{2} - f_{1}) R = {MR}^{2} \times \frac{a_{Cm}}{R}$

f₂ – f₁ = Ma_cm

f₁ = f₂ – ma_cm = 1.4 – 2 × 0.3 = 0.8 N

$0 .8 = \frac{P}{5} \Rightarrow P = 4$

Note : It has been assumed that the stick applies horizontal force of 2N (only normal reaction)

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