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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 ( $m < < M$ ) which are at rest. There are n number of particles per unit volume. The cylinder moves in a direction perpendicular to its axis. Assume that the particles do not interact with each other and bounce with same speed after hitting cylinder. The drag force per unit length of the cylinder require to maintain the speed v constant for the cylinder is $\frac{K}{3} n m R v^{2}$ Find the value of K?

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answer is 8.

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Detailed Solution

In the frame of the heavy cylinder the particle comes in with speed V and then bounces off.

$f = \int_{- \frac{π}{2}}^{+ \frac{π}{2}} 2 m v \cos^{2} θ (R d \cos θ) l v n \frac{f}{l} = \frac{8}{3} m v^{2} n R$

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