Question

A coin is placed on a horizontal platform, which undergoes vertical simple harmonic motion of angular frequency ω. 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 of g/ω²

(d) for an amplitude of √g/ω

Answer 1

Correct Answer is: (a, b)

Let O be the mean position and a be the acceleration at a displacement x from O.

At position I, N - mg = ma. ∴ N ≠ 0

At position II, mg - N = ma.

For N = 0 (loss of contact), g = a = ω²x.

Loss of contact will occur for amplitude x_max = g/ω² at the highest point of the motion.