A cylinder of mass M and radius R moves with constant speed v through a region of space that contains dust particles of mass m which is at rest. There are n number of particles per unit volume. The cylinder moves in a direction perpendicular to its axis. Assume mlt ltM, and assumes the particles do not interact wilth each other. All the collision takes place is perfectly elastic and the surface of the cylinder is smooth. The drag force per unit length of the cyliner require to maintain the speed v contant for the cylinder is K/3nmRv^(2). Find the value of K?

A cylinder of mass M and radius R moves with constant speed v through

1.	A cylinder of mass M and radius R moves with constant speed v through a region of space that contains dust particles of mass m which is at rest. There are n number of particles per unit volume. The cylinder moves in a direction perpendicular to its axis. Assume mlt ltM, and assumes the particles do not interact wilth each other. All the collision takes place is perfectly elastic and the surface of the cylinder is smooth. The drag force per unit length of the cyliner require to maintain the speed v contant for the cylinder is K/3nmRv^(2). Find the value of K?
Answer» Solution :In the FRAME of theheavy CYLINDER the PARTICLE comes in with speed `V` and then BOUNCES off. `f=int_(-(pi)/2)^(+(pi)/2)2mvcos^(2)theta(RD thetacostheta)lvn` `f/l=8/3mv^(2)nR`.

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