A mass of `2.0 kg` 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 pressed slightly and realeased the mass executes a simple contant is `200 N//m`. What should be the minimum amplitude of the motion, so that the mass gets the detached from the pan? `(Take g= 10 m//s^(2))`

Options

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

Answer

B

Explanation

Let the minimum amplitude of SHM is `a`. Restoring force on spring
`F=Ka`
Restoring force is balanced by weight `mg` of block. For mass to execute simple harmonic motion of amplitude `a`.
`:. Ka= mg`
or `a=(mg)/(k)` Here, `m = 2kg, k= 200N//m, g= 10m//s^(2)`
`:. a=(2xx10)/(200)=(10)/(100)m`
`=(10)/(100)xx100 cm= 10 cm`
Hence, minimum amplitude of the motion should be `10 cm`, so that the mass gets detached from the pan.