A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency `omega`. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

Options

A. for an amplitude of `g^(2)//omega^(2)`
B. at the highest position of the platform
C. at the mean position of the platform
D. for an amplitude of `g//omega^(2)`

Answer

D

Explanation

The coin will lose the contact with the horizontal platform, if the amplitude of osciallation (A) of the vertical oscillation is such that in the topmost position, the maximum force `[mAomega^(2)]` is more than the weight (mg) of the coin.
In limiting equilibrium, `mAomega^(2)=mg`
`therefore A=(g)/(omega^(2))`