First slide

Force

Question

In gravity- free space, a particle is in contact with the inner surface of a hollow vertical cylinder and moves in horizontal circular path along the surface. There is some friction between the particle and the surface. The retardation of the particle is

Easy

A

zero
B

independent of its velocity
C

proportional to its velocity
D

proportional to the square of its velocity

Solution

Normal reaction N is the only radially inward external force acting on the particle $\large \therefore N=\frac {mv^2}{r}$
Frictional force f_k is horizontal and tangential.f_k = µ_k.N = µ_k.mv²/R
$\large \therefore f_k\propto v^2$

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