suppose in thought experiment a box with negligible mass is isolated from any other mass . An elastic spring is attached to the ceiling of the box while other end carries certain mass . The box is uniformly accelerated alternatively in direction from lower end of the spring towards ceiling and then in direction from ceiling towards lower end of spring .Will there be any tension in the spring in both the cases?

Due to inertia the object with mass will resist any change in speed when the box is accelerated, so the spring will be alternatively stretched and compressed.

 

You don't need an isolated box of negligible mass to try this out, just take an elevator ride and you can feel the difference when the elevator starts and stops.

thank you very much indeed for the reply

If the same experiment is performed in lift which is falling down freely with acceleration g or moving upwards with acceleration g will there be compressing and stretching of the spring?Suppose the lift is not experiencing any external gravitational field , will the tension in the spring be equal to mg where m is the mass attached to the end of spring?

thank you very much indeed for the reply

If the same experiment is performed in lift which is falling down freely with acceleration g or moving upwards with acceleration g will there be compressing and stretching of the spring?Suppose the lift is not experiencing any external gravitational field , will the tension in the spring be equal to mg where m is the mass attached to the end of spring?

 

Acceleration and gravity are indistinguishable; things inside an elevator sitting still and one accelerating at g will behave exactly the same.