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

Answer

C

Explanation

The net offect of these two forces must be toward mean position
At the mean position , there is no net and hence normal reaction equalls `mg` Above position normal reaction is less than `mg` and below mean position normal reaction is greater than `mg` At the top extreme

`N` is minimum at the top exterme
Net fprce toward mean position `= ma = m omega^(2)A`
`rArr mg - N_(1) = m omega^(2) A`
`N_(1) = N_(min) = mg - m omega^(2)A`
For loosing contact with the plateform `N = 0`
so `A = g//omega^(2)`