Question

A small coin is placed on a flat, horizontal turntable. The turntable is observed to make three revolutions in $\pi s$. What is the coefficient of static friction between the coin and the turntable, if the coin is observed to slide off the turntable when it is greater than 10 cm from the centre of turntable?

• A. 0.45
• B. 0.6
• C. 0.5
• D. 0.37

Answer 1

The correct option is D 0.37

The friction force on the coin balances the centrifugal force to 10 cm.
Now, frictional force on coin is given by $\mu mg$
And, centrifugal force is given by $mr{\omega }^2$
$mr{\omega }^2=\mu mg$
where, $\omega =\frac{\theta }{t}=\frac{3\times 2\pi }{3.14}=6degrees/s$
Thus, centrifugal force = $m\left(0.1\right)6^2$ at that point.
Equating the two, we get,
$\mu =\frac{m\left(0.1\right)\left(36\right)}{m\left(9.8\right)}\approx 0.37$