Q. A coin is placed on a horizontal platform, which undergoes horizontal SHM about a mean position O. the coin placed on platform dies not slip, coefficient of friction between the coin and the platform is$\mu$. The amplitude of oscillation is gradually increased. The coin will begin to slip on the platform for the first time
A) at the mean position
B) at the extreme position of oscillations
C) for an amplitude of $\mu$g/$\omega^{2}$
D) for an amplitude of g/$\mu{\ \omega}^{2}$
Explanation
(c) Let $O$ be the mean position and $x$ be the distance of coin from$O$. The coin will slip if centrifugal force on coin just becomes equal to force of friction $ie,\ mx\omega^{2} = \mu mg$
The coin will slip if $x =$ maximum $=$ amplitude $A$
$\therefore\ \ mA\omega^{2} = \mu mg\ \ or\ \ \ A = \mu g/\omega^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.