Rotation 3 Question 21

27. 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/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 P10. The value of P is

(2011)

Analytical & Descriptive Questions

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Answer:

Correct Answer: 27. 3.6

Solution:

There is no slipping between ring and ground. Hence f2 is not maximum. But there is slipping between ring and stick. Therefore, f1 is maximum. Now let us write the equations.

I=mR2=(2)(0.5)2=12kgm2N1f2=ma or N1f2=(2)(0.3)=0.6Na=Rα=RτI=R(f2f1)RI=R2(f2f1)I0.3=(0.5)2(f2f1)(1/2) or f2f1=0.6N Further f12+f12=(2)2=4f1=μN1=P10N1

Solving above four equations we get, P3.6



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