A light, flexible rope is wrapped several times around a hollow cylinder with a weight of 40 N and a radius of 0.25m that rotates without friction about a fixed horizontal axis. The cylinder is attached to the axle by spokes of a negligible moment of inertia. The cylinder is initially at rest. The free end of the rope is pulled with a constant force P for a distance of 5 m, at which point the end of the rope is moving 6 m/s. If the rope does not slip on the cylinder, what is the value of P

The value is

Explanation:

From the question we are told that

    The weight of the hollow cylinder is  

     The radius of the hollow cylinder is  

       The distance which it is pulled is  

       The velocity of the end of the rope  is  

Gnerally the mass of the hollow cylinder is  

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Generally angular displacement for the distance covered is mathematically represented as

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Generally the torque experienced  by the hollow cylinder is mathematically represented as

Here I  is the moment of inertia

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Generally from kinematic equation

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Generally the  final angular velocity is mathematically

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Generally the  initial  angular velocity is Zero given that the hollow cylinder was at rest before rolling

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=>  

a and b sometimes have a positive value

at right angles to each other