A mass of 2kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in figure. The mass of the spring and the pan is negligible. When spring is pressed and released the mass executes a simple harmonic motion. The spring constant is `200 N"/"m`. What should be the minimum amplitude of the motion so that the mass gets detached from the pan? (take `g= 10 m"/"s^(2)`)

Options

A. `10.0 cm`
B. less than `12.0cm`
C. `4.0 cm`
D. `8.0 cm`

Answer

A

Explanation

When pan reaches at maximum displacement then mass and pan gets detached
At this position `mg- m omega^(2) a=0`
`therefore g= omega^(2)a`
`therefore a= (g)/(omega^2)= (mg)/(k)`
`therefore a= (2xx 10)/(200)`
`therefore a= (1)/(10)m = 10 cm`.