Question

A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of $3.5$ revolutions per second. A coin placed at a distance of $1.25cm$ from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is : $(g=10m/s^2)$

• A. $0.5$
• B. $0.3$
• C. $0.7$
• D. $0.6$

Answer 1

The correct option is D $0.6$

Magnitude of limiting friction between any two bodies in contact id directly proportional to the normal reaction between them.

$f_l=\mu R$

where

$f_l=$ Limiting friction

$\mu =$ Coefficient of friction

$R=$ Reaction force

In equilibrium

$m{\omega }^{2}r=\mu mg$

$\mu =\frac{{\omega }^{2}r}{g}$

$\omega =2\pi \nu =7\pi rad/sec$

$r=1.25cm=1.25\times {10}^{-2}mg=10m/s^2$

$\mu =\frac{49{\pi }^2\times 1.25\times {10}^{-2}}{10}=0.6$