Question

A coin is placed on a horizontal platform, which undergoes vertical SHM of angular frequency $\omega$. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

• A. at the highest position of the platform
• B. at the mean position of the platform
• C. for an amplitude $g/{\omega }^2$
• D. for an amplitude $\sqrt{g/\omega }$

Answer 1

Answer: (A), (C)

at the highest position of the platform
for an amplitude $g/{\omega }^2$

The coin will leave contact at any point when the acceleration of platform is more than 'g' and in the same direction of 'g'. At the highest point, both of the conditions are satisfied. Acceleration at the highest point is equal to ${\omega }^{2}A$, so we have
${\omega }^{2}A\ge g$
$\Rightarrow A\ge \frac{g}{{\omega }^2}$