A mass m=1 kg is put on a flat pan attached to a vertical spring fixed on the ground.When pressed slightly & released ,the mass executes SHM.What is the amplitude A of the motion so that the mass m tends to get detached from the pan.(Given k=500 N/m & g=10) 1)A=1.5 cm 2)A<2cm 3)A=2cm 4)A>2cm

at the highest point of the motion (that is at the topmost end of the amplitude after which the pan moves downwards due to the pull of the spring), the normal force on the block must be zero. only then the block will tend to get detached because left free on its own the block will have a maximum downward acceleration equal to g but the pan can move with a greater acceleration on account of the spring pulling it. so for the block to get detached its acceleration of the pan at the highest point must be greater than or equal to g. this gives 

Aw² > g

this gives A > 2cm.

note that w is the angular frequency of the SHM which is equal to (k/m)^1/2 and g is the acceleration due to gravity.